If any other form of hunting is prohibited from a car and there is nothing that specifically states that car hawking is legal then I think you would be pushing your luck trying it. Sooner or latter you would probably get written up for it.
In Nevada i have asked 3 game wardens and all stated the same thing. "I don't see why it would be illegal but i will research it" if you have any questions ask the people who might restrict it. I think it would all come down to the individual game warden.
It Is Unlawful • To hunt game from any motorized vehicle, except for holders of a valid handicapped persons Motor Vehicle Hunting Permit. Also see page 50 (use of motorized vehicle) and see below (Unlawful methods of take “From boats . . .”).
Read it however you want but it seems pretty clear cut to me.
I will assume you are thinking of car-hawking a kestrel at starlings or English sparrows, both non-game not protected species.
The problem is how a C.O. would read this. Be sure to deal the public in on this hand. If someone thinks you are doing something wrong they will drop a dime.
My advice is to go to your Id Fish & Game regional office and ask to speak with the chief enforcment officer.
