No; the loss on the sale of a personal residence, or other personal use property, is not deductible. The question of who actually sold the property is not important since neither of you can claim a loss.
If there was a gain, on the sale, tax reporting would get a little sticky and would best handled by cooperation. But, so did the sharing of the proceeds. But, unlike the sharing of proceeds question, there is a way to report the gain without getting the courts involved (the IRS might still have to act a judge).
