Most all insurance contracts contain provisions stating how long you have to file a claim or suit against the company. This is known as a Contractual statute of limitations. If you do not file a claim or a lawsuit within this time period, you may lose all rights to recover for your claim.
For example, your policy may state that you have one year from the date the claim arose (the date the injury or accident occurred), or from the date the claim was filed, or from the date the claim was denied, to file suit. This however is for first party claims with your own insurance company.
Making a third party claim typically means you are need to abide by the statute of limitations set by the state. That being said even with a third party claim the at-fault party's insurance company will still want you to make the claim within a reasonable amount of time since if you put off making the claim more damage could be done to the car, if there were witnesses they may be hard to track down or for them to remember the accident and the each driver's memory of the accident has likely deteriorated.
California requires an injured person to file a claim for personal injuries within two years of the date of the injury. So personal injury claims (or lawsuit) must be made within 2 years per the California Code of Civil Procedures Section 335.1, 340.
The Statute of limitations in California for a property damage lawsuit or claim is 3 years. But once again the sooner you make the claim the better so that the memory of the accident is clear in the driver's minds and the adjuster can see that there was no other damage sustained since the incident with their insured.
California has a fair claims settlement regulation in place for consumers. As part of this regulation auto insurance companies must acknowledge a claim, start investigation, provide forms and instructions, and provide reasonable assistance immediately but in no event later than 15 days after receiving notice of claim. (Notice of claim is any written or oral communication to the insurance company which reasonably apprises the insurer that you wish to make a claim.)
They must also respond to communications received from you immediately but in no event later than 15 days. An insurance provider must accept or deny the claim immediately but in no event later than 40 days after receiving proof of claim.
Proof of claim is documentation in your possession which provides any evidence of the claim and supports the magnitude or the amount of the loss such as estimates of repair or police report indicating theft of your vehicle, et cetera.
It is a good idea to file your claim as soon as you can. If you wait to place a claim with your insurance company or a third party claim with another insurer, you may need to explain on why there was the delay. Also the adjuster may want to take a more comprehensive look at your vehicle to make sure no other damage was done after the accident and before the claim was placed.