(CNN) -- Trayvon Martin's parents will ask the U.S. Justice Department to review a local Florida prosecutor's interactions with police investigating the teen's shooting death, the family's lawyer said.
The Justice Department launched an investigation into Martin's death on March 19, but the family is now asking it to look for possible interference by State's Attorney Norm Wolfinger's office with Sanford, Florida, Police Detective Chris Serino, attorney Ben Crump said.
The Martin family will send a formal request to the Justice Department Monday, Crump told CNN Sunday.
Martin, 17, was fatally shot by neighborhood watch volunteer George Zimmerman, 28, after Zimmerman called police to report him as a "suspicious" person on the evening of February 26.
Zimmerman says he killed Martin in self-defense after the teen punched him and slammed his head on the sidewalk, according to an Orlando Sentinel report that was later confirmed by Sanford police.
Police cited Florida's "stand your ground" law, which allows people to use deadly force anywhere they feel a reasonable threat of death or serious injury, for not immediately arresting Zimmerman.
Authorities have said Zimmerman was not immediately charged because there were no grounds, at the outset, to disprove his account that he'd acted to protect himself. Martin's family and supporters say Zimmerman, who is Hispanic, racially profiled the teen, who was black, and ignored a police dispatcher's directive not to follow him.
The killing sparked nationwide protests, including a march Saturday by civil rights luminaries, carrying "Justice for Trayvon" signs in a marching to the Sanford police headquarters.
The Sanford police department has come under intense scrutiny for its actions following the shooting, and protesters renewed their call for the firing of police Chief Bill Lee, who stepped aside temporarily this month amid criticism.
The local prosecutor also stepped aside. Gov. Rick Scott appointed a special investigator to decide if Zimmerman should be charged, cleared or if the case should be sent to the grand jury.
CNN's Vivian Kuo contributed to this report.