The line from Annie Hall was taken from his standup routine.
From his standup routine:
"I'm not a fighter. I, ah, I have bad reflexes, and I can't fight. I was once run over by a car with a flat tire, being pushed by two guys. And I was not in the army, in case you were wondering. I was in the canine corps. Strange story, when I was young, I wanted a dog, and we had no money, we were very... my father at that time was a caddie at a miniature golf course in Brooklyn, y'know. I couldn't get a dog, 'cause it was too much, and they finally opened up in my neighborhood, in Flatbush, a damaged pet shop. They sold damaged pets at discount, y'know, you could get a bent pussycat if you wanted, a straight camel, y'know. I got a dog that stuttered. When the cats would give him a hard time, he would go 'B-b-b-b-bow wow', y'know. He'd turn all red, y'know. We wanted to send him into the army, but the papers got crossed up, and they got me instead of him. I was in the canine corps for two weeks. Me and eleven dogs was the outfit. Taught me how to heel. Sergeant was a little Mexican hairless, y'know. I was not in the regular army. I was classified '4-P' by the draft board, we went to war, I'm a hostage."
From Annie Hall:
Alvy Singer: They did not take me in the Army. I was, um, interestingly enough, I was, I was 4-P. Yes. In the, in the event of war, I'm a hostage.
The best I can make of this line and what it meant was...because he was not in the regular army, he was in the Canine Corps, in the event of war, his role was to be a designated Prisoner, as he was classified by the draft board when mistakenly assigned to the Canine Corps. I have to guess 4-P was for being unfit for Army Service (4) and being disignated a Prisoner (P).
I do love his line about having bad reflexes, and getting run over by a car with a flat tire being pushed by two guys.