Being a Ranger, I do LE and am an EMT-B along with most other LE rangers.
But when I was a city cop it was very different. I volunteered with the fire dept and worked as a cop. The guys were always giving me crap, asking if I was sure I didn't just want to work on the "dark side."
But my little PD used to be a combined department and the older cops remembered their EMT stuff. Once I brought the ambulance on scene to CPR in progress and there was one officer holding open the door for us, and Sgt. Hayden (whose good advice is in my signature) was down on the floor with the fire chief (who'd responded from home) doing CPR.
Didn't help, rarely ever does (as someone else already mentioned), and Sgt. Hayden got vomit on his pants, but I would rather be in the middle of things than holding the door. Not that there's anything wrong with just holding the door.
In life's small things be resolute and great
To keep thy muscle trained: know'st thou when Fate
Thy measure takes, or when she'll say to thee,
"I find thee worthy; do this deed for me?"
Nemo me impune lacessit.