Regardless of whether your car is leased, financed or wholly owned, if it's been in a collision, the at-fault party is responsible for all damages, including diminished value. Diminished market value can be determined by taking it to two or three dealers and having them give you an estimate of its value after fully disclosing the collision damage. Have them provide the estimates in writing on dealership letterhead with the name and phone number of the person estimating the market value.
The claim must be made within 3 years of the collision, and typically it has to be made concurrently with any other claim (property damage, bodily injury). In other words, you get one opportunity to settle all of your claims. The release that you sign when you settle will typically cover all claims.
Only the claimant will receive the money from a diminished value claim, unless there is a total loss. If a total loss occurs the titled owner will receive the claim settlement. When the lease is up, the leasing company should be on notice regarding the collision, and will take that into account with all other damage, mileage overages, etc. in determining what the difference is between the car's actual market value and previously assessed market value. Check your lease agreement to determine how that will be handled.
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