Yes, in and around many areas, I don't know if they still have them but in metro areas there used to be armed merchant patrols that would police merchant areas. I know of manny communities that are not a city, but have private police forces.
I know of few places that have private police but the police get sworn in by a local police force as some agreement they have
But as for as signing over your rights, the HOA ( or even some housing districts in historical areas) can tell you what color you can paint your home, if you can have any yard decorations.
I know of one where you can not have a pick up truck parked outside the garage, you can not leave your garage door open longer than so many minutes and never over night. Some of the gated communities require even your guests to check with security before they can enter.
But you sign away rights when you get a drivers license, you agree to take a breath test if they request you to. And you can lose your licesne if you refuse, even if you had not had one drink.
