No, your existing rifle is not exempt from the AW laws.  You would need to purchase an LEO-restricted rifle with department letterhead, and that rifle remains restricted (you can only sell it to FFLs and other qualifying LEOs, and must dispose of it to the above if you quit/retire).  The letterhead must state that the rifle is allowed by the deparment and is for duty use, but once you have it, it's legal to use it on your own time as well.  The same basic rules apply to restricted post-ban hi-cap mags.

-Troy