When Alexandria city officials reopened a police investigation into bingo operations in the city this spring, they deliberately kept the probe a secret from city prosecutor William H. Cowhig, The Washington Post has learned.

The decision to bypass Cowhig came after Police Chief Charles T. Strobel complained in an April 4 memo to City Manager Douglas Harman that Cowhig had said "there was no need to continue" the police investigation even though the probe, according to Strobel, "revealed that certain improprieties did occur" in the games.

The specific case referred to in the memo from Strobel dealt with games run in a building leased by a company controlled by one of Cowhig's former law clients, Edward L. Hinkle Jr. It has been disclosed previously that Cowhig also had declined to prosecute another former client for alleged bingo law violations.

City Manager Harman said yesterday that in light of Cowhig's inaction concerning the initial police investigation, which ran from November 1977 to January 1978, "I didn't inform the commonwealth's attorney about the (reopened) investigation I requested. I thought it was more appropriate that the police department conduct its investigation and render its conclusion without the involvement of the commonwealth attorney's office," Harman said.

Strobel said his office sometimes conducts investigations without informing the office of the city's chief prosecutor. Harman and Strobel declined to state why they excluded Cowhig this time, since he had requested the initial investigation.

Shortly after the Strobel memo to Harman, a copy of which was obtained by The Post, a police undercover officer obtained employment as a secretary to Alva Ford Thompson, who since has been indicted on felony gambling charges connected to bingo operations. Kathleen Bralove, the officer, worked for Thompson from April 13 to May 11 and, according to a court affidavit, said that Thompson bragged that he took "500 off the top" of the games profits and falsified data given the games sponsors.

In his memo to Harman the chief wrote that, "It has been established that bingo operations are highly profitable and are controlled by a select few. This is concerning to us in that it very well could be a breeding grounds for an organized effort to make quick and unreportable financial gains."

The original investigation by police focused on "certain alleged improprieties" occuring at a bingo hall at 3819 Mount Vernon Ave., Strobel wrote. The alleged improperieties included bingo games conducted without permits, rental fees that were in excess of the building's fair market value for similar properties in the area, an improper accounting of funds, and use of paid employes. All four are illegal under Virginia's bingo law.

Cowhig has said in interviews that he has told city officials that it is the duty of police and others to regulate and investigate bingo operations. He called in April for appointment of a special bingo prosecutor amid charges he was lax in pressing charges against game operators.

Cowhig said he told Harman tht he believes the state bingo law may be unconstitutionally vague.

The bingo hall referred to by Strobel was leased by its owners to Landlord Investments Inc., a Virginia corporation controlled by Hinkle and Robert L. Gerber, according to state records.

In 1958, Cowhig had acted as the attorney for Hinkle in setting up the Bi-Me Company, Inc., a real estate firm. In 1966 Cowhig, then still in private practice again had acted as the attorney to reinstate the real estate firm when its charter apparently was inadvertently allowed to lapse, according to state records.

Cowhig said yesterday that his relationship to Hinkle was strictly a legal one. Hinkle could not be reached for comment.

In January, Cowhig turned aside a city official's request for "appropriate action" against another one of his former law clients. Cowhig then wrote a letter to city finance director, Howard J. Holton, saying James Fike, bingo operator, "has assured me that (he) will no longer operate a bingo game without the necessary permits."

Cowhig had represented Fike in the 1972 formation of B & J Specialties, a firm Holton said conducted unlicensed bingo games. Fike was indicted along with Thompson by a grand jury last week on alleged gambling violations.

Additionaly, a U.S. grand jury was empaneled on Monday to investigate the possibility of bingo and currency violations, and the possible corruption of elected officials. The grand jury ended the initial phase of its investigation in Alexandria yesterday after hearing from Hinkle. The jury is expected to resume its work in September, according to an official in the district court clerk's office.