According to the police report, Tanguma called 9-1-1 around 9:30 Tuesday morning.
He told dispatchers he woke up and discovered he had "smothered" his 4-month-old daughter in his sleep.
The report also stated Tanguma cooperated with Lubbock police detectives, agreeing to go to the police station and be interviewed.
In that interview he told detectives he had been fired from his job on Monday and was "very stressed."
Tanguma said he fell asleep late Monday night watching television, but was awakened several times because his daughter was crying.
Sometime before 10:00 a.m. Tuesday morning, he said the infant was screaming so loud, he began to get angry.
Tanguma told police he laid the 4-month-old down on a futon and grabbed her throat with his hand and squeezed "very tight."
He said the baby continued to cry and at that point he "placed his hand on her torso and pushed hard several times in a downward compressing motion."
Tanguma said the child stopped crying.
Tanguma told police he "must have fallen asleep at some point" and when he woke up the infant's lips were blue and she was limp.
That's when he called 9-1-1 and EMS arrived.
Tanguma is in the Lubbock County Jail, charged with murder.
His bond has been set at $500,000.