No. Normally, you're not able to cancel a claim once it is made to the car insurance company.
With car insurance, how a claim is handled depends on state laws and terms of the policy involved. In general, though, if you start a claim but then decide to take care of the damage yourself, you aren't able to cancel the claim but can ask that it is closed out without payment being issued.
For instance, say you back into your mailbox and put a dent in your car and automatically call your car insurance company to make a collision claim. After making the claim, you think about it and get an estimate for the damage and find out that the cost of repair is just a little more than your deductible amount.
In this situation, you likely would like to cancel your claim and just pay out-of-pocket for the repairs. You can call your auto insurance provider and see if that is possible, but usually what they will tell you are that instead of canceling the claim, and acting like it never existed, they can only close it out and note that no payment was made for the damages.
Even if you are able to close out a claim in this manner, it will still show on your claims history that a claim was made, just that no payment was issued. It then may or may not affect your car insurance rates.
If it is not a physical damage claim (collision or comprehensive) that you want to cancel, but instead a liability claim, then it is doubtful that the claim can even be closed out without payment, unless the investigation shows no damage or injuries were incurred.
If you have a claim you want to cancel or close out now without payment, you need to contact the claims representative assigned to the claim and find out if that is possible at this point in the process.
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