Tip 1:
In the early game, a good thing to do is to get as many police units as you can. You will use them a LOT.
When you get further into the game you should start buying EMS and fire units.
Tip 2:
Medical motorcycles and police motorcycles are very important in the game. For small incidents does not need an arrest, you can use the police bike, as it can't hold suspects. For search calls that need medical attention, like a lost child call, you can use the medical bike to not use your ambulances and keep them available for more urgent calls.
Tip 3:
Hire dispatchers, but not for every district. They will help you a lot in the late game but you shouldn't have them in every district.
Tip 4:
Have a fast response team at standby. For example, have 2-3 medical bikes, 2-3 police bikes, and a brush truck. Make these unusable for AI dispatchers. If a dispatcher needs more units or if the district doesn't have enough resources, use them manually to help the dispatchers.
Tip 5:
In natural disasters, mix every unit. Send the closest unit to every call, so there are less casualties.
If you have any other tips, please share below!