Although Chen Yu really wanted to turn the murderer over to the police and have him pay the price he deserved, without evidence, the police wouldn't believe what he said. Therefore, he had to wait for the murderer to recover, at least to regain consciousness and be able to speak before he could take any action.
Otherwise, pointing at a patient in a coma and calling him a murderer would lead the police to think Chen Yu was mentally ill.
Despite the dissatisfaction, since he had decided not to take the law into his own hands, he had to abide by legal procedures and act accordingly.
However, Chen Yu still tampered with the murderer in secret, accelerating the healing of his wounds so he could wake up faster while also casting a curse on his soul, plunging it into an endless nightmare. The murderer was forced to experience the pain felt by those he had killed, a small measure of revenge and punishment.