Helicopters can fly in heavy rain or any rain without any problems as long as the helicopter pilots visibility is not reduced.
If the rain is heavy enough to cause poor visibility then the helicopter pilot may decide it's too dangerous for them to fly in the rain.
Or if a bad thunderstorm is near or is occurring then the helicopter may stay on the ground and wait the storm out just for safety.
In an emergency situation such as for a life flight then the helicopter may be able to fly but not always.
It takes time for the helicopter to get started up before they can actually take off so for a life flight helicopter it can sometimes be faster to get the patient to the hospital in an ambulance.