What kind of emergency and with which type of radiation or source? It depends if you are dealing with sealed or unsealed sources. First of all the intervening personnel has to be equipped with electronic dosemeters in order to monitor the doses. Then if it is about unsealed sources in nuclear medicine a goal is to keep the contamination local, which means if you have to decontaminate the patient or the personnel do it in the room, where the contamination occurred, then bring the patient out. I would need more details on the scenario for further counsel.
This should be a question for the local Radiation Protection Officer (RPO). A specific answer is difficult (see other responses), but in generally speaking, it depends on who might receive which doses in the given case.
In general, every case has a different scenario depending on the type of source and radiation which it is emitting and activity with its physical properties, the first thing is to check the dose using survey meter (dose meter) to get a safety for the workers by using a suitable shield, distance and time when dealing with this case. the second is by asking about the details of the radioactive source.
Radiological incidents are not like other hazardous incidents where the best response is to immediately exit the area. In a medical setting, most (I say that cautiously) activity levels from a single source are not high enough to cause immediate external harm but can cause harm if the space around the spilled or leaking source is occupied for long periods and/or personel are very close to the source without proper shielding or inhalation protections... all of which should have been accounted for during the authorization process BEFORE the source was used. If the source is a radiation producing machine, the solution is simple... cut power to the machine. If the source is dispersible, don't panic and start running around as this could cause more contamination. Without knowing the source in mind, the best thing to do is block off access to the spill and call your local radiation safety officer immediately, who will give you further instructions. If a radiation detector is immediately availible, use it to check yourself for contamination and dispose of the contaminated articles in a designated bin. After that (in general) pretty much just stay a safe distance from the source and try not to touch anything until help arrives or instructed to do something else.
Generally speaking, each hospital has at least one person responsible for radiation protection. As part of risk management, procedures must be in place at each facility to ensure that those affected by the incident know immediately what to do in a particular type of emergency. It all depends on the type of facilities, the type of treatment performed (nuclear medicine, radiotherapy, etc.).