The incident took place at the Calder Square Apartments in the 100 block of North Calder Drive in League City.
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Two Galveston County Precinct 4 Constable deputies were trying to serve the woman a possession order, according to Constable Justin West.
As deputies approached, they said the woman left the apartment without any clothes and threatened the deputies with a box cutter.
That's when smoke began to billow from the apartment, according to West.
One of the deputies was able to take the woman into custody.
Everyone was evacuated from the building as fire crews quickly doused the blaze and arson investigators were called to the scene.
Officials said they believe the evicted tenant deliberately started the fire.
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League City Fire Chief Michael Lugo said a downstairs unit was heavily damaged by the fire. The woman living inside of it was critically burned.
Another individual living in a unit above also had to be taken to a hospital for injuries, according to Lugo.
Firefighters rescued one dog from the apartment, but found the body of another animal inside, though West said that animal had been dead for some time well before the fire.
The evicted tenant could face charges connected to the attack on the deputy, as well as the possible arson. These possible charges are pending the outcome of the woman's physical injuries and a mental health evaluation.
No firefighters or law enforcement were injured.