Rock Hudson tells a funny story about this scene in "Doris Day - Her Own Story". He says that he had trouble carrying Doris around for as long and as far as required, hence the special shelf. Then he goes on:
I could have managed if only one take had been involved, but we went on endlessly, primarily because there was a bit actor who played a cop on the street, and as we passed him Doris's line was "Officer, arrest this man," and the cop was supposed to say to me, "How you doing, Brad?" but that stupid actor kept calling me Rock. So back to our marks we went for another take and another and another. I'll bet we did that scene twenty times. That's why the shelf for Doris to sit on.