Depending on the state and and crime, the best answer is you need to file a police report "as soon as possible". Even though there are lots of reasons you may not file a police report immediately - such as retribution, needing to rest and recover, or protecting a family member, it is also very true that every day that you don't file a report makes it less likely that you will remember crucial details that may lead to an arrest. The start of a police investigation of a crime is triggered by filing a police report. If an investigation doesn't start soon after a crime is committed, witnesses may forget key details or evidence may be tampered with or become contaminated.
Statutes of Limitations
There is a statute of limitations on every crime. This sets the rules, or governs, how much time may pass before charges may not longer be filed. This ranges from one year for small offences such as vandalism, traffic accidents or minor theft to no statute of limitations for serious felony offences such as child abuse, rape or murder.
A general rule is that petty offences have a one year statute of limitations, two years for misdemeanors, and felonies have a 5 (five) year statute. States may differ - some may set the start date at the time the crime is discovered to have occurred, but the majority begin at the moment the crime is committed. If you were to discover some property vandalism 6 months after it occurred, you will likely have much less time to file your police report.
Always try to report a case as soon as you can. Just because you have 1, 2 or 5 years under the statute of limitations, police need time to investigate, and prosecutors need time to prepare their case. If you are unsure how to file a police report, the police officers can assist you with the process.
Some states require that citizens report incidents like traffic accidents to police within a few days. This is because evidence that is crucial to the case can disappear quickly and police may have little to nothing to go on if you don't tell them what happened. Make sure you research the reporting laws in your state to see if these requirements apply to you.