Investigation
As the investigation began Conan noticed that smell coming from the corpse was weird for the circumstances of the crime. This crime was committed by strangulation by rope. The smell was gunpowder, which is usually omitted when a gun is fired. So, the victims cause of death and evidence doesn't evidently match up. Ran noticed that parts of her make up was missing and the face was wet.
During this time a potential suspect comes into the scene. Osamu Samon the victim's fiancé. He explains his relation to he victim and also introduces another suspect, Toshihiko Migita. As they were going to question the second suspect, Conan and Osamu were in the back seat and Osamu showed him a photo of a party that was held for him by his school students. He tells Ran that he knows the dying message could potentially refer to him.
This shows a lot party poppers fired at Osamu Samon
As they question Toshihiko Migita, it is shown by him that Osamu is also a definitive suspect, but Toshihiko has a solid alibi, the video surveillance footage. As everyone reviewed this footage, Conan spotted many flaws with footage that point Toshihiko as the culprit. Firstly there is no time stamp on the footage which can be easily manipulated to the culprits advantage, Secondly a part in the footage where Toshihiko disappears for a moment and reappears, he claimed he went to the toilet. This triggers a doubt in Toshihiko's alibi, in Conan's mind, but up to this moment there isn't a clear indication to who is the culprit. Inspector Yamamura and Kogoro Mouri point to Osamu Samon as the culprit, due to lack of an alibi. At this moment Osamu Samon doesn't have a clear motive for killing the victim and Toshihiko Migita's alibi has many flaws that hasn't been identified by Inspector Yamamura and Kogoro Mouri.
Conan steps out of the shop to review where everything stands and who could be the culprit. As he looks around he notices shards of glass and a damaged concrete wall, this clears up many misconceptions Conan may have had, he follows up with the necessary procedures to gather up information on this incident with the broken wall. In the shop Inspector Yamamura is about to take Osamu Samon as the culprit, Conan bursts on the scene and knocks Kogoro out cold to begin the 'The Sleeping Kogoro's deduction show'.
Deduction
The evidence that Conan gathers is as follows:
Toshihiko Migita: The flawed surveillance footage with him disappearing abruptly and reappearing slightly different, The shards of glass and broken concrete outside his shop and finally the dying message.
Osamu Samon: His emotional relationship to the victim as a fiancé, The image on his phone with the party poppers and finally the dying message.
Victim: The dying message that resembles the top part of the kanji for "left" (左) or "right" (右), her wet face with some of her makeup removed and finally a smell of gunpowder on her clothing.
Explanation
The dying message wasn't intended to point towards Osamu Samon as the culprit, but it was for Toshihiko Migita as it was him. When writing Migi you write the horizontal bar after the sweeping stroke, when looking at the dying message it was shown accordingly. So it wasn't the katakana 'na' nor 'Samon', only 'migi' is written in that order. The surveillance footage, Toshihiko was in view of the cameras for the period it was running, though we assume that the cameras are always left running. Toshihiko used that preconception... The time he left for the toilet is when he turned the cameras off. Then, he took the scooter on a 10 minute trip to the crime scene, and attacked the victim. It took him another 10 minutes to return, he turned the cameras back on and reappeared within it field of view. Using that technique even if there was more than 20 minutes missing, it would appear as there was no gap at all, as this camera system doesn't display a time stamp for the footage it would be easy to manipulate. This is the testimony of a student that lives nearby:
" It was around 10:30. There was a program I wanted to watch, so I turned on the TV. Then..." (There was an accident involving a white 4-door car crashing into the wall and then driving off. He shows picture of the car on his phone with the time stamp of '22:30')
It was most likely a drunk driver. The car might be in the vicinity of this area, it would be a white car with a broken headlight. If Toshihiko was in the shop he could have heard the crash clearly and would have reacted on the surveillance footage, but he never paid any attention to the noise in the footage. Why? Because the footage from that time was missing. 10:30 matches the time of the murder. Toshihiko Migita wasn't present at that time. What tipped Kogoro (Conan) off was his hair, which was messy as he was going to the toilet, but when he came back it was neatly flattened as if he was wearing a helmet. Toshihiko Migita motive was because the victim apparently harassed him with photos of her current relationship. Then made fun of him by saying she never sent them.
Inspector Yamamura receives a call confirming that there is gunpowder residue on the victims clothes. This is usually found when the victim is shot by a gun but Toshihiko didn't kill the victim with a gun but the victim died of strangulation by rope. The culprit for the victim's death isn't Toshihiko Migita it is Osamu Samon, now this can contradict Kogoro's (Conan's) deduction as he explain that the stroke order of the dying message did indicate that Toshihiko was the culprit. The dying message did indicate the truth, the truth that the victim never wrote the dying message but Osamu Samon did. Now, if you consider the dying message, It could have never been written by the victim as if you see the victims email you would see that the victim writes Toshihiko Migita's name differently in katakana. So why would she write Toshihiki Migita's name in kanji in her final moments. This proves that Osamu is the murderer as when you think to when Toshihiko wrote his name and compare it to Osamu way of writing the dying message it identical to the way Osamu has written it.
Let's start from the beginning, the first step of Osamu's plan was to send Toshihiko harassing emails from the victims smartphone. Knowing Toshihiko's personality and misguided affection towards the victim. Osamu took advantage of Toshihiko to tempt him to murder her. The style of the emails sent by the victim never had any punctuations such as 'commas and full stops', and always ended in her signing her name 'Nana', but the emails sent to Toshihiko had punctuations and didn't end in him signing her name. It isn't easy changing the style you write in, the same goes for the stroke orders. It was obvious the they were written by someone else. That's how Osamu's plan succeeded, just as he planned Toshihiko attacked the victim with clouded judgements of hatred. Osami headed to the park, when he saw her collapse to the ground he was certain, his plan succeeded but, something unexpected happened, she wasn't dead and she managed to get up and was her face to clean away the dirt. That's why the victims face was wet with the make up rubbing off. That is when the final blow was given to finish her off and write the dying message "Migita", but then he heard Kogoro, Ran, Conan approaching in car so he had to rush away from the scene. The proof behind that is the gunpowder residue, the reason why gunpowder residue was found in a crime that didn't involve a gun was because of the photo. The photo contains evidence of party Osamu had which involved a lot of party poppers, as you may guess due to there gunshot like sound they contain gunpowder, the same gunpowder residue left on the victims clothes and Osamu's clothes. The gunpowder transferred to the victims body as he strangled her to death. If Osamu says he didn't meet her on that day how can he explain the gunpowder on her at the crime scene.
The motive for Osamu's crime was because she called of the engagement, Osamu was wearing a ring but the victim wasn't, which meant Osamu's feeling was unrequited.
To conclude Toshihiko Migita is the culprit for the attempted murder of the victim.
Osamu Samon is the culprit for the murder of the victim.
