Galveston police said they were called to the resort property at 4:30 a.m. after hotel guests reported hearing "pops" from one of the rooms on the eighth floor.
When police arrived, the hotel room was locked and a faint moaning was heard inside. When they forced their way in, authorities say they found a man and two boys - ages 10 and 5 years old - on the bed with gunshot wounds.
Police also found a woman on the floor who appeared to have been shot as well.
The man, who police identified as Mauricio Morales, and one of the children were pronounced dead at the scene. The woman and the other boy were taken to University of Texas Medical Branch hospital where they died.
Police said evidence indicated the woman may have shot her husband and their two kids before turning the gun on herself.
Police added the deceased family members from Baytown checked in to the hotel around 7 p.m. Sunday.
Authorities have not yet released the names of the woman and the two boys who were killed. A neighbor of the family, though, identified the woman as Flor De Maria Pineda De Canas.
Goose Creek ISD confirmed the children attended classes at Victoria Walker Elementary School.
The school district released a statement following word of the boys' deaths.
"The tragic circumstances surrounding these students' deaths are almost too much to bear," said Goose Creek ISD in a statement. "A student death can have a ripple effect on a school community and, because of this and out of concern for the students' classmates and the campus faculty, we will have additional counseling services at the school. We are grieving for the loss of young life and its infinite possibilities and we pray for the family, friends and students most affected by this tragedy."
Capt. Joshua Schirard, of the Galveston Police Department, said they are not looking for any suspects.
"Our thoughts are with the victims and their family members during this difficult time. We are still gathering information about this isolated incident, however it appears to have been a murder suicide amongst a family in their room," said Paul Schultz, Vice President of Hospitality for Landry's Inc. "We are fully cooperating with the police department during their investigation and will assist them in any way we can."
Landry's Inc. owns the San Luis Hotel and Conference Center.
Police have no immediate word on a motive for the killings.
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