The Missouri Department of Insurance site only declares that you should immediately report your accident or circumstances that will cause you to file a claim to your insurance company or agent. If you were not at fault the MO DOI says to report the accident to the other driver's insurance company immediately as well.

You should file your claim within a reasonable amount of time so that your insurance or the other person's insurance company can properly investigate the incident. If the state does not have time limits it is likely that there are time limitations set up by the insurance company in your policy contract that you signed. Contact the insurance company or the DOI to find out more specifics.

In regards to the police report it is generally up to each jurisdiction to decide how long they will come out to take down a report. You will need to speak with your local law enforcement establishment to find out if you have to report it that same day or can make a report 7 to 14 days later or even more.