Most of the work in this field can be done with a pair of trauma shears. I think you will find that knife will remain unused for the most part.
The one situation that I can think of that would require a blade with a good length cutting edge is to cut through rope in an attempted suicide case (hanging person.) I am sure there are other uses but I can't think of them offhand. Something small and out of the way like a spyderco serrated delica or the H1 steel salt series if you anticipate a lot of exposure to sweat.
Although I do not carry one myself a leatherman type multi tool could come in handy a lot of times (pliers for 02 tank and screw driver bits for odd and ends.)
Although a lot of EMTs carry cutlery in pouches (not a good idea in my opinion) I would recommend carrying concealed you may run into people you wouldn't want seeing let alone reaching for your blade if a scuffle should happen.
I have a Cold Steel rescue that sits in my bag unused for the most part as well as a Vic Swiss Army tinker that is used once in a while, for the screw drivers usually, this also sits in my bag.
I wouldn't even dream of bringing anything with a sharp edge inside a mental health lockup or correctional facility. If you forget to remove it from your person before going in, I would want it to remain out of sight.
I happen to love the looks and feel of large tacticool types of knives but on the job I think they would just be an extra burden to carry and keep track of.