Yes, an insurance claim can be made without a police report or the police reporting to the scene. And, under Ohio law, you have a duty to provide your insurance information to him. If you refuse, he could end up filing a lawsuit against you. You should probably contact your insurance company and let them know about the accident immediately. Most policies require that you notify them of any accident as soon as possible after the accident. And you should probably follow their advice as to how you proceed from here, so that you dont violate the terms of your insurance policy.
Best of luck.