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The landlord's claim for damages is as any other claim, and the landlord has the burden of proving the liability and amount of damages.
If you do not agree with the landlord's estimate of damages (you have stated that you do not dispute liability) you have the right to dispute or sue the landlord for amount claimed or demand that the landlord substantiate the amount claimed. In other words, the landlord can be challenged and forced to meet a burden of proof
Here is the relevant statute:
RCW 59.18.280Moneys paid as deposit or security for performance by tenant — Statement and notice of basis for retention — Remedies for landlord's failure to make refund.
Within fourteen days after the termination of the rental agreement and vacation of the premises or, if the tenant abandons the premises as defined in RCW 59.18.310, within fourteen days after the landlord learns of the abandonment, the landlord shall give a full and specific statement of the basis for retaining any of the deposit together with the payment of any refund due the tenant under the terms and conditions of the rental agreement. No portion of any deposit shall be withheld on account of wear resulting from ordinary use of the premises. The landlord complies with this section if the required statement or payment, or both, are deposited in the United States mail properly addressed with first-class postage prepaid within the fourteen days.
The notice shall be delivered to the tenant personally or by mail to his or her last known address. If the landlord fails to give such statement together with any refund due the tenant within the time limits specified above he or she shall be liable to the tenant for the full amount of the deposit. The landlord is also barred in any action brought by the tenant to recover the deposit from asserting any claim or raising any defense for retaining any of the deposit unless the landlord shows that circumstances beyond the landlord's control prevented the landlord from providing the statement within the fourteen days or that the tenant abandoned the premises as defined in RCW 59.18.310. The court may in its discretion award up to two times the amount of the deposit for the intentional refusal of the landlord to give the statement or refund due. In any action brought by the tenant to recover the deposit, the prevailing party shall additionally be entitled to the cost of suit or arbitration including a reasonable attorney's fee.
Nothing in this chapter shall preclude the landlord from proceeding against, and the landlord shall have the right to proceed against a tenant to recover sums exceeding the amount of the tenant's damage or security deposit for damage to the property for which the tenant is responsible together with reasonable attorney's fees.
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