punt n.
An act of punting.

1. Rugby Football. A kick given to the ball dropped from the hands, before it reaches the ground. (Cf. drop-kick, place-kick.) Also in other varieties of football.
2. transf. An upward jerk. rare.


OED2

The citation is the 1845 Rules book from Rugby Scool. I can imagine a possible way this sense of booting a ball might come to get transferred to rejecting something in a more general way, but p'raps your version comes from some other source entirely? Hell, it is SoCal...