Bloomberg is no longer a Republican. He originally was registered as a Democrat, then decided he wanted to run for Mayor but the Democrat primary was crowded, so he changed his registration to Republican, where competition was much less in the primary. After Republicans became unpopular (around 2006), Bloomberg changed his registration to Independent. Currently, he has his face up Obama's a**.
Whatever his party registration this week, Bloomberg is still a much bigger target for the Attorney General than a county sheriff in Arizona.