Let me just point something out here: You don't shoot unarmed people at range who have made no moves against you. That's not doing your job as a good police, that's attempted murder.
Romy was out of line. Batman could have reacted better, but seriously, SHE. SHOT. HIM.
Her partner even thinks she overstepped herself, and he was out of the room when it happened. As far as he knows, she could actually have been defending herself, and his first reaction is still "Dude. You shot BATMAN! WTF??"