May 1, 2013  -- A deaf Texas couple have been charged in the beating death of their 5-month-old daughter who was allegedly killed after an argument about who would care for the crying infant.

Hector Rene Cupich-Quinones, 35, and Maria Guadalupe Zuniga, 37, of Richardson, Texas, have been arrested and charged in the death of their baby. Both parents are deaf and mute.

"It's sort of been my understanding that they can somehow detect or feel these vibrations and stuff like that and you still have some hearing, but not something to where you can make out anything," Richardson Police Sgt. Kevin Perlich told ABCNews.com. "They could sense when the child was upset and crying."

"Anybody would know if a child was crying or not," Philadelphia Children's Hospital pediatrician Dr. Cindy Christian told ABCNews.com. There are the tears and the babies make faces, so there are visual cues to crying aside from the sound.

Christian said that for deaf parents the trigger for frustration could be seeing the baby constantly crying or feeling the baby's distress when they hold the child.

"People who can hear would think that if you couldn't hear the crying, it would be less frustrating because what triggers us it that sound," Christian said. "It was probably something about what that baby was doing that triggered the same frustration and those feelings [in the deaf parents]."

Cupich-Quinones has been charged with capital murder and Zuniga has been charged with injury to a child.

Richardson police responded to a report of an unresponsive child around 5:30 a.m. on Sunday. When they arrived, the father had the child in his arms and the baby was "pale, not breathing, and had bruises on her arms," according to a police search warrant.

The officer performed CPR until paramedics arrived and took the child to a hospital. The hospital reported that the child had suffered "massive trauma to back of the head, bruising to the child's back, chest, and both arms," according to the warrant.

The baby died at the hospital.

"It was pretty bad, certainly something children shouldn't have to go through," Perlich said. He did not know if the child was deaf.

In an initial interview, using an interpreter, Cupich-Quinones told police he had gotten up around 3 a.m. to get a drink of water and noticed the child lying on the living room floor near the small day bed the baby slept in. He said the child was faint of breath so he woke up his wife and eventually contacted their interpreter who called the police.

His story would soon change.

Another deaf man who lived at the house, Charles Niel, indicated to police that their search should include the backyard where there were beer cans and whiskey bottles.

"Niel pointed at the couple and then put his hand to his mouth indicating they had been drinking," the police report said. Police found the beer cans, whiskey bottles and other containers of alcoholic beverages at the house, according to the search warrant.

When the couple were brought to the police station for additional interviews, police said Cupich-Quinones voluntarily waived his rights and agreed to answer questions.

He allegedly told police that he and his wife had been drinking and had gotten "into an argument over the child crying."

He said he tried to give the child to Zuniga but she was "too intoxicated" and would not take the child.

Police say the father told them that he was holding the baby with both hands around the torso and shaking the baby at around 12:30 a.m. He allegedly told police he "hit the back of the child's head on the kitchen counter at least three times," according to the report. He also allegedly struck the child's face, knocking her off the counter and onto the kitchen floor.

He told police he then left the infant with Zuniga who allegedly put the baby to bed and went back to her room to sleep. Cupich-Quinones said he went outside to smoke a cigarette and then went back to bed. He stated that at around 3:30 a.m., he woke up and began to argue with his wife about who was at fault for hurting the baby.

The argument allegedly went on for two hours before police were called.

"Hector Cupich-Quinones admitted that his assaultive actions caused the death of the child and took full responsibility for committing this offense," according to the police report.

After being read her rights, Zuniga invoked her right to counsel and did not provide a statement to police.

Both parents are being held at the Dallas County jail. The father is being held on a $1 million bond and the mother is being held on a $750,000 bond.

Police did not know if the couple had retained an attorney and Dallas County officials did not respond to request for comment.