Actually there are 2 that I know of. One is A Stitch in Crime where he gets very angry with Dr. Mayfield (Leonard Nimoy) in his office, and slams down a coffee carafe. And the other is An Exercise in Fatality where he is in a hospital waiting room and he really has it out with Milo Janus (Robert "tight pants" Conrad).
Ok...I think you are thinking of How To Dial A Murder. Great Episode. There were actually 2 dogs and their names were Laurel and Hardy. The rosebud thing was their "kill command" word. They would attack upon hearing that word.