When Dejean-Jones kicked the bedroom door, the man shot him with a handgun, the statement said.
Dejean-Jones collapsed in the apartment's breezeway and died at a hospital. The shooting is under investigation, police said.
Dejean-Jones was "believed to be breaking into the apartment of an estranged acquaintance" but entered the wrong one, the apartment complex manager said in an email to residents obtained by Dallas NBC television station KXAS.
Sources told ESPN that Dejean-Jones was in Dallas to celebrate his daughter's birthday and got into an argument with the child's mother before the shooting.
Dallas ABC television station WFAA quoted sources as saying that Dejean-Jones' girlfriend lived in the apartment complex.
His agent, Scott Nichols, told ESPN that Dejean-Jones died from a gunshot wound to his abdomen.
A 6-foot-6-inch (1.98-meter) guard from Iowa State University, Dejean-Jones had averaged 5.6 points and 3.4 rebounds in 14 games with the Pelicans.
He made his NBA debut in January. Dejean-Jones, a native of Los Angeles, had signed a multi-year contract with the New Orleans club in February.
"We are devastated at the loss of this young man's life who had such a promising future ahead of him. Our thoughts and prayers are with Bryce's family during this difficult time,” the team said in a statement.
(Reporting by Ian Simpson and Frank McGurty; Editing by David Gregorio and Paul Simao)
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