The shooting death of a member of Edie Brickell & New Bohemians appears to fall under state law permitting deadly force in self-defense, police said Tuesday.

A grand jury will decide whether the man who shot Jeffrey Carter Albrecht will be indicted, but Sgt. Larry Lewis said Dallas police aren't pursuing charges.

Police said Albrecht, 34, was inebriated and had been fighting with his girlfriend Monday before he was shot by a neighbor of the girlfriend.

The neighbor, who was not immediately identified, woke up around 4 a.m. to his wife screaming that someone was breaking into the house, police said. The neighbor yelled through the door for Albrecht to leave and then fired his handgun through the door, hitting Albrecht in the head.

"He yelled several verbal warnings, 'I'll shoot! I'll shoot!'," Lewis said. "From what we gather, he fired near the top of the door, hoping he would scare the person away."

The homeowner, whose identity wasn't released, was not arrested.

The shooting came two days after the enactment of a new state law, nicknamed the "Castle Doctrine," that gives Texans a stronger legal right to defend themselves with deadly force in their homes, cars and workplaces. Police and prosecutors, however, said the shooter appeared to be protected under an earlier law that allows a person to protect their property with deadly force to "prevent the other's imminent commission ... of criminal mischief during the nighttime."

"In an incident like that you're well within your rights under the old law, as well as the new one, to use deadly force," Dallas District Attorney Craig Watkins said.

Albrecht, who went by his middle name, had been a keyboard player for New Bohemians since 1999, according to the band's Web site. His death stunned friends and those who knew him in the North Texas music community.

"I am heart broken," Edie Brickell wrote in an e-mail to The Associated Press on Tuesday.

"We are all completely devastated by the news of Carter's death, and obviously still quite in shock," Brandon Aly, drummer for New Bohemians, wrote in another e-mail.

Albrecht played several times with Brickell's husband, Paul Simon. He also played with Texas musician Charlie Sexton, a renowned guitarist.

He also played keyboard and guitar and sang for Sorta, named in 2006 as the best local music act by the Dallas Observer.

Edie Brickell & New Bohemians scored a breakout hit in 1989 with "What I Am." They broke up for several years but regrouped and put out an album last year.