The case is actually murder, and the culprit is Seiko Kanbayashi. The Kanbayashis merely pretended to be happily married, but their life together has long since gone to shambles, and they have become interested in different partners. Chosaku had been hatching a plan to kill his wife to reap in her life insurance, but he wasn't aware that Seiko was trying to do away with him as well.
Chosaku originally planned have the documents sent to his wife to make her come to him. Then he would pretend to leave his office for cigarettes, then go into the neighboring building to open a bathroom window on the fifth floor. After returning to his office (for an eyewitness testimony), he intended to jump from his building into the bathroom next door, intercept Seiko in the park which she was sure to walk through, and strangle her. Then he would return the same way and deliver his manuscript, again with an eyewitness, thus consolidating his own alibi.
While on the works to provide his alibi for his wife's murder, however, Seiko (with the intention to carry out her own murder plan) arrived early, spotted Chosaku behaving strangely, and realised what he was up to. The moment when he jumped from one building to the other, she was already waiting inside the bathroom and hit his face with a deck brush in mid-jump, causing the facial scars. With his momentum so abruptly stopped, Chosaku fell into the alley between the two buildings to his death. Seiko returned later and pretended - with the doorman of Chosaku's office building as her alibi witness - to be the first discoverer. Her crime could be proven thanks to her hair being found in the bathroom from where she killed her husband, and Chosaku's eyebrow hairs among the bristles of the brush.