The Atlanta Police Dept. tells TMZ ... they DID NOT give Reese Witherspoon a free hat after her arrest -- in fact, cops say the "A.P.D." cap she was wearing this weekend is nothing more than a CHEAP, UGLY KNOCKOFF!
We spoke to Senior Officer Stanionis from the Public Affairs office of the APD, who told us point blank -- "We did not give her that hat. We have no idea where she got that hat."
"In fact, that’s an awful hat," Stanionis continued ... "Looks like a patch glued onto a hat and it’s not a good one."
Wearing a phony police hat??? That is beyond ...