The answer for your question will differ depending on what state you have an accident in. There are variations in state and sometimes even local laws regarding collisions. The general answer is that a police report must be filed if there is any a death, personal injury or property damage that exceeds a certain dollar amount, typically $200 to $1000.
For example in Illinois the driver involved in a crash must report it if the collision involves death, bodily injury or property damage over $500. In Wisconsin you are required to notify the police immediately if the accident involves injury, death or property damage of $1000 or more. In NJ the amount of property damage has to be $250 or more to any vehicle or other property.
You will need to get a copy of your State's driver's manual or handbook from Department of Motor Vehicles (DMV) similar agency to get the answer for your specific state.