Please note that I am only licensed in the State of New York and this is for general information purposes only.
The absence of a police report does not necessarily mean that you do not have a viable case against the owner/driver of the offending vehicle, however, it is highly recommended that you file one as soon as possible with the precinct in which the accident occurred.
The driver should have already put State Farm on notice of the accident, but it is advisable that you contact the insurer as well to give them basic facts of the accident and the damage to your vehicle.
In this type of situation it is always preferable to file a police report about the incident. It may also be advisable to take photographs of the damage.
As you are dealing with an insurance company known to be rather hard-nosed, it may be advisable for you to obtain your own independent estimate of the damages to your vehicle. Be wary of attempts to use aftermarket replacement parts which do not come from the manufacturer of your vehicle. If you have difficulties dealing with any carrier, you may wish to file a complaint with your state's Insurance Commissioner's Office.
The at-fault-driver is still responsible for the damage to your even whether or not a police report is filed. However, it is advisable to go forward and file your own report and obtain photographs of your vehicle (even if State Farm has taken pictures). Go and obtain insurance and then file the report. You need to have insurance on your car even if you are not driving it.
Report the accident to State Farm and explain what happened. If they ask you for a recorded statement, you do not have to give one--you can, but I typically recommend politely telling them no and offering to explain what happed without a recording. Then, call several body shops of your choice to evaluate the damage to the vehicle. Good luck.
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