My son moved back home from Texas two weeks ago. He is mentally ill and I need him to move out of my home because he is causing problems in my home. The local police say I have to file formal eviction papers. Is this true or can I just tell him to go stay somewhere else now?

You can always just tell him to leave, but legally he does not have to. And you can not just kick him out. If you tell him to leave and he does, great but if he does not leave you will have to file formal eviction notice, and then if he still does not leave, file in court.

With that said, depending on his mental condition you may have trouble kicking him out real fast and the courts may give him extra time because of his mental issues

I am not so sure the police are right, after only 2 weeks in your house. Usually establishing residency is 30 days. And having an illness doesn't mean he gets to stay either. He should be able to be escorted off the property as an unwanted guest, a trespasser. Many a parent though gives a grown child a bus ticket or 3 nights in a Y and says go. You can lock the bedroom and put a chain around the fridge and make living there as unpleasant as possible, and if he causes damage or hurts anyone, then you can have him thrown out.

I gather that he refuses any mental health help and that you have tried to get him into a halfway house, or disability benefits and housing, and so on? Is he so ill that you are going to be seen as a horrible parent?