Couple of questions.
Is he in jail awaiting trial on the charges?
Was bail set?
If he is in jail awaiting trial, and bail was set, then that still applies. If he was not given bail pending a psych e v a l, then after the psych e v a l he will have a bail hearing (maybe).
In the federal system, a person deamed incompetent to stand trial would be sent to a federal facility where they will work to get the person to a mental level that they would be competent, then they would be returned to the US District Court for trial. They may, or may not be free on bail / release conditions after being found competent. Worst case scenario is that the individual ends up with an insanity ruling and goes to a mental hospital (never gets convicted).
I wouldn't move right away unless that is actually a real option (selling house? Don't let the prospective buyer know that your neighbor is who he is) let the justice system work.
Hope this helps.