I have even joked and kidded with the dead themselves at scenes. Truthfully, I have done some of my best shtick talking to dead bodies. OK, they don't laugh, but they also never interrupt.
The real lesson in all this is that you need to keep that odd sense of humor. You will need it to make it through this wonderful profession. If you are a cop five years or more, you will have lived more life than the average citizen could ever know. But to cope with that experience, you will need to laugh.
Just remember, there are some things that are too terrible to laugh about. I will not talk about them here, but when such things happen around us or to us, the moment is often too tragic or too sacred to even joke about. In those moments, we just need each other, and it will be your caring, not your humor, that will make the difference.
Finally, in case you were worried, the bicyclist survived with only minor injuries. The paramedic turned to us as he was leaving and asked us for the story in detail. His response was, "Shame is, he would have been a hell of a donor." I answered, "Yep, in great shape and he doesn't smoke," then turned to look at my partner's cigarette firmly clenched in his teeth.