I would imagine that your home State has the same procedure as New Mexico.
Whenever I took someone to jail I had to have an arrest warrant or a criminal complaint, signed by me. There were no exceptions unless it was an illegal immigrant then ICE would fax a hold order directly to the jail. Until they got the order I just sat there waiting because they would not accept any prisoner without documentation. Also the prisoner would be given a copy of the warrant or criminal complaint. You MUST have been given some paperwork.