San Francisco police leaders committed to changing how the department handles sexual assault and rape investigations at a City Hall hearing Thursday, as supervisors pressed them over persistently low case-clearance rates and concerns about whether investigations comply with state law. Nearly 100 people attended the three-hour hearing, called by Supervisor Myrna Melgar and several colleagues and organized with the Commission on the Status of Women. Melgar opened by citing findings that SFPD’s clearance rate for these cases was less than half the national average and among the lowest in California. She also pointed to findings that the department had systematically failed to investigate sexual assault cases as required by state law. Police Chief Derrick Lew, Assistant Chief Nicole Jones and Special Victims Unit Captain William Toomey answered questions from supervisors. Lew said the department took the concerns seriously and acknowledged that it needed to improve. “We also come to this conversation with humility,” Lew said. “There are things we believe we are doing well, and there are areas where we know we need to get better.” The hearing drew eight of the city’s 11 supervisors. Public Safety and Neighborhood Services Committee members Danny Sauter, Bilal Mahmood and Alan Wong were joined by Melgar, Jackie Fielder, Connie Chan, Chyann Chen and Matt Dorsey. Supervisors Rafael Mandelman, Stephen Sherrill and Shamann Walton did not attend. The police leaders’ commitment signals a response to sustained scrutiny of how sexual violence cases are handled. The information presented at the hearing did not specify a timeline or detail the changes the department plans to make.