How long after an offer is denied on house does the escrow agent/title company have to return your escrow deposit to you?

If there is no dispute over the escrow funds between the buyer and seller, the escrow agent/title company should return the deposit on demand. You may want to have an attorney draft a demand letter. Given the circumstances described, it is unlikely that the title company would delay disbursement.

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They should release the earnest money upon your demand. There is no dispute over who owns the money and the contract was never accepted; therefore, it's your money. You may either leave it in escrow as you shop for other homes and simply have your Realtor inform the listing agent that earnest money has already been accepted and deposited (as long as you put the same amount of earnest money in the future offers) or you can request that the money be released to you.