Mad Dog was a henchman working for Two-Face.
History
Mad Dog served as a liaison between Two-Face and Gil Mason. He was part of the fake murder attempt on Mason, but Batgirl interfered. The two came to a fight, in which Batgirl managed to pull off Mad Dog's ski mask. He got away when he kicked her into a dumpster.
Barbara looked up his face in police records and began suspecting Mason of foul play when she saw Mad Dog in his house the next day. He later reported the events of the previous night to Two-Face, unaware that Matches Malone was listening in on their conversation. When Malone followed Mad Dog to Two-Face's lair, he was knocked out.
Two-Face and his thugs took him to an abandoned subway station, where they questioned him. Robin and Batgirl showed up, but the gang escaped. Mad Dog sealed off the entrance with two grenades.
With plans kicked into overdrive, Mad Dog busted James Gordon out of City Jail. He took him to Bayshore, where Mason and Two-Face planned to kill him, had Batgirl not arrived. When Batman arrived moments later, Mad Dog took him on. Though he fared better than the other henchmen, Robin threw him off the pier into the wharf.