Police are searching for those responsible for the damage discovered Sunday on the statue at the entrance to Queen of Peace Roman Catholic Church.
The Galveston County Daily-News reported Monday that parishioners discovered the markings of what appear to be two cross-like drawings and a message stating the statue was not Jesus. Some markings are on the forehead of the statue bought by church members about a year ago.
Parishoner Alex Mendez said church members will clean the graffiti.
La Marque is 30 miles southeast of Houston.