That is so cool! It indeed is a 409 car because it has the numerals above the cross-flag emblem. Also those wheels appear to be 15", not the normal 14".

I remember reading about the LAPD police car specs in some old 1966 magazine. They talked about how the cars were spec'd and the reasoning behind it. Typically they would not go for the hottest engine, they would spec a 396 when available, a TH400, manual steering (!) and heavy duty everything. That '64 probably has a 340-horse 409 with hydraulic lifters and loads of torque.

Those old bias-ply tires would roll and decrease the contact patch in hard cornering, but that meant they were toss-able, controllable and would break away gradually. Radials on the other hand did not gradually reduce the contact patch and would grip in corners until the traction limit was exceeded, then traction was lost and broke away suddenly. When radials finally lose traction there is no recovery.

Shown below is a '64 Biscayne cop car with a 327 (no numerals) and 15" wheels: