At least the Maryland State Lodge of the FOP does; as they signed onto an amicus brief arguing in favor of Heller in DC vs. Heller.
This does bring up an issue that is near and dear to my heart, as both my father and I have been in law enforcement in different capacities, and I have a lot of friends that are in military law enforcement or civilian LE. While you’re often going to hear police chiefs and Sheriffs calling for more gun control, more often than not the rank and file officers just don’t support gun control. Ask a guy like LawDog how many crimes he’s seen that could have been prevented if the intended victim was armed and trained; hell as almost any cop you meet.
I will say that a sort of exception are “big city” cops, people like LAPD and NYPD, which will probably have more anti-gun officers than in say, Indianapolis Metro Police Department. I don’t blame that on the department, but rather the area, because it follows that demographically speaking you’d have more anti-gun officers in an anti-gun area.
Remember that a Chief of Police is 99% of the time a political appointee of the Mayor of a city; which means that if he wants to keep his job, he’ll toe the party line of the mayor. Your average street cop won’t say anything to the media often about supporting the right to keep and bear arms unless he works for an administration that supports the right, because he also wants to keep his job.
If you’re friends with the local Five-O, talk to some of them, and see how they feel about the 2nd Amendment and the right to keep and bear arms.