I was looking at Yoreh De'ah 340:5 (יו"ד סימן ש"מ ס"ק ה) and Moed Katan 25b (כה עמוד ב), which require Kriyah (garment-rending) for all who are there at the time of death. It would seem to me that an EMT, EMS member, doctor, nurse, or any other emergency first responder who is there at the time of death must rip Kriyah for all the places they respond to when a death of a Jewish patient occurs. Also a doctor who regularly see patients die must tear Kriyah every time, as he can lose many patients in a single day (oncology, cardiology). What is the approach with ripping Kriyah in these cases?
Nit'ei Gavriel (Aveilus 4:4) cites various sources that there is a common practice to not tear kriyah in this instance anyway (and in note יב he mentions other variations, such as leaving a button undone for a while, or tearing kriyah at the moment of death only for a distinguished person).
In 4:7 he also writes that it is indeed not customary for doctors or nurses to tear kriyah, and in note טז various reasons for this are offered - although he also cites a statement in the name of R. Moshe Feinstein that indeed they do need to do so.
I will find the source later but one only has to tear kriya when they are present at the time that a person dies. Additionally one only has to tear kriya on clothing that you own. If you are wearing a uniform owned by the hospital (scrubs) or are a paramedic wearing uniforms issued by the company than you are exempt. I was a paramedic for many years. My rav at the time paskened that I should tear kriya only if wearing my own shirt and the person who died was a Jew.
See the Tzitz Eliezer 13:35 section ד on this page.
I know of one doctor who did it when he was present when a Jewish patient died (and there was no family present). Not sure of any standard procedure or the like beyond that.