The family of music executive Chris Lighty is sounding off about the investigation into his death. Lighty, 44, died in August at his home in Riverdale of an apparent self-inflicted gunshot wound. Lighty’s family, along with 50 Cent and others, in September hired lawyer Scott Leemon and P.I. Les Levine to help probe his untimely death. Leemon alleges that eight months later, the NYPD hasn’t done a thorough investigation, calling the police efforts “cursory at best.” Leemon wrote in a statement yesterday that a medical examiner never tested Lighty’s hands or clothes for gunshot residue, even after taking samples from the scene. Leemon also writes that the gun found at the scene was traced to a “multi-gun purchase in North Carolina,” and was “never reported stolen.” Despite this, “No follow-up was done with this information.” Leemon and Lighty’s mother, Jessica Brooks, are asking the Bronx district attorney to investigate. “The family just wants answers,” Leemon told Page Six yesterday. “Wherever the facts lead, they just want answers. All we want to do is see what happened here.” Brooks has launched a petition at ipetitions.com to gather public support to urge the DA to take up the case.