In my experience, it's always a tough decision whether or not to get the police involved at the scene of an accident. Typically speaking, you will call the police from the scene of the accident and they will ask you whether or not anyone was injured. If there are no serious injuries, most people say, "No." Truthfully, if no one has any immediate serious injuries, the inclination might be to say "No, there are no injuries." If that is the case, the police will generally advise you just exchange information and go on your way.
However, many insurance adjusters will use the lack of police report at the scene as evidence against you if you later claim injury from the car accident. That can backfire if you discover your injury at a later date. In fact, some serious injuries can manifest themselves later on, once all the adrenaline has passed etc. Of course, you don't want to mislead the police officers into thinking you have an injury when you don't. By the same token, you don't want to be extra brave and foolish by declining police assistance at the scene if you have some possible injury. In fact, this is not the time to be brave and "suck it up." It is however time to document the injury and the accident. Again, so many insurance adjusters will use the lack of the police report against you - as evidence you were not injured since the police did not take a report. Therefore, think long and hard before you decline assistance from a police officer at the scene of accident.