Sorry it took me so long to get back on line and give the answer. Anyway, the connection I was looking for is that both The Cheap Detective & The most Crucial Game have female characters that speak with a Russian accent and try to hide it from Peter. I knew it was a little esoteric. Sorry. I thought my "rushin'" clue might help.

that was a good clue...the 'rushin' thingy...

I can think of a very general (probably TOO general) one, and that's that it has a detective who (though he's a "tough-talking" one) never shoots or even (I think) hits anyone (even though he makes Paul Williams beat HIMSELF up!). But one thing that occured to me even before this question is that the Ann-Margret character accidentally gives away an East European accent, like Valerie Harper's character in "The Most Crucial Game." Could that possibly be one?