Grace Saenz-Lopez apologized Friday to Alice residents and said she believed her actions were in the dog's best interest.
"I am sorry for the division that the events of these last few weeks have caused," Saenz-Lopez wrote in her resignation letter. "It was never my intention to bring any negative exposure to our city."
A custody hearing Monday is expected to decide who gets Puddles, who Saenz-Lopez renamed "Panchito" after taking the dog last summer.
A neighboring family accuses Saenz-Lopez of refusing to return the dog after leaving it in her care while they went on vacation. A day after her neighbors left, Saenz-Lopez called to tell them Puddles had died.
Three months later, a relative of the neighbors saw the pet at a dog groomer. When Saenz-Lopez refused to return the dog, the family filed a criminal complaint and a civil lawsuit against her.
Homero Canales, who represents Saenz-Lopez, has said his client believed the dog would die if returned to her neighbors.
Saenz-Lopez, the city's mayor since 2003, was indicted Jan. 18 on two felony counts of tampering with evidence and concealing evidence.
Those charges came after Saenz-Lopez filed a police report claiming the dog was missing. The dog was later spotted at the home of Saenz-Lopez's twin sister, in Ben Bolt, about 10 miles from Alice.
City commissioners voted unanimously last week for a resolution urging Saenz-Lopez to resign. Mayor Pro-Tem Juan Rodriguez will take over mayoral duties.
Alice is about 45 miles west of Corpus Christi.