House decree/ house deed

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My exwife was entitled the house completely on the decree.  Once the divorce has finalized, she decides to attempt sale of our home.  I had a verbal agreement with her, that we would split in half, any equity the house would earn time of sale.  She has petitioned me to court, so she can have soul ownership to sell our home.  If I don't sign the home deed over to her.  Can she still sell our home?