Can I be prosecuted for stealing even if there's no proof?

Recently I was at a party with a roommate and a kid lost his iPhone. The next day they traced it using GPS back to our apartment building. He is convinced we took it but I have no idea where this kids phone is. He told us if we don't return it to him he will prosecute. We have already dealt with the cops and had them search our house and nothing. No clue where this kids phone is but I don't have time or money to get prosecuted. Can he do this?

He can't prosecute - the state does. If the police won't press charges then there's no case. He can try to sue you, but he doesn't have any evidence.

You have nothing to worry about. He has no evidence and will get nowhere if he tries. I do not think the case will even be heard in court if he brought it up.

You can be prosecuted if the police and DA believe him and feel they have enough for a case. That doesn't mean they'd win. It isn't likely to happen if what you said in your posting is all that they have.

They can't prosecute you unless they have proof you either tool the phone or have possession of it.