The Alexandria City Council voted last night to hold private and public discussions of the city's troubled police department, citing alleged mishandling of an unsolved murder case, low morale within the force and the relationship between police and the prosecutor's office.

The private session will be held Jan. 9 and will focus on personnel and legal problems within the department. A public discussion is set for Jan. 16.

City Councilman Robert L. Calhoun, saying the department had been given "an extremely bad rap" in the press recently, said the council wanted "to know how they (police) function." Calhoun also cited what he called "irresponsible statements" made by a former police officer on the department's problems.

Calhoun was referring to former investigator Joseph Soos, who quit the force last month saying police had mishandled a suspect in the unsolved slaying of socialite Donita Cutts.

Cutts, 388 was found beaten, bound and gagged July 29 in the burned-out basement of her Wolfe Street town house. Her slaying has remained a mystery to her friends and neighbors in the affluent Old Town section.

Soos, a nine-year veteran of the force, said the handling of a possible suspect was "the final straw" in a series of recent failures by the department to "live up to the high standards" needed in police work.

Alexandria police have come under fire recently for their use of civilian volunteers in massage parlor and drug investigations. Those investigations resulted in strained relations between police and the commonwealth's attorney's office when cases were either dismissed on grounds of governmental misconduct or dropped by the prosecution.

Additional criticism of the city's police last night came during a public hearing on a proposed ordinance designed to put massage parlors out of business.

Frederick W. Ford, an attorney for health club owner Hamers Kibler, accused the police department of "conspiracy and criminal solicitation" in its use of a civilian volunteer to gather evidence against massage parlors.

Ford said his client wants indictments brought against high-ranking police officals and members of the vice squad

He attacked police use of the civilian, which led a General District Court judge to dismiss a case against a masseuse at one of Kibler's clubs on Aug. 31.

Ford also told the council that Kibler wants police officials prosecuted for "conspiracy to injure another in his trade, business or professin," a misdemeanor.

Councilman Calhoun warned Ford that he was "treading on very dangerous ground."

The council enacted part of its massage parlor ordinance last night-limiting hours of operation to 9 a.m. to 5 p.m. and requiring establishments to keep lists of patrons-and plans to consider further requirements and restrictions on Saturday.