There is no evidence that a former Alexandria housing authority director illegally used a secret $700,000 investment fund that went virtually undetected for more than a decade, the city's prosecutor concluded after a three-month investigation.

Commonwealth's Attorney John E. Kloch said this week in a letter to City Manager Douglas C. Harman that he was "satisfied there is no evidence of criminal activity" on the part of Harland K. Heumann, director of the agency until a reorganization in 1977.

The issue arose in the spring when new housing director Angus Olsen discovered the $700,000 fund after a $73,000 interest check landed on his desk. Heumann had deposited the money, Olsen learned after tracing the check, in certificates of deposit at five banks. The accounts had slipped from the agency's main budget ledger in the 1977 reorganization, Olsen found.

Interest checks, Olsen said at the time of the discovery, came as frequently as every three months but were virtually unnoticed by everyone except one employe who had been instructed by Heumann to record them in a separate ledger.

Heumann used the accounts as a "personal petty cash fund," Harman alleged in June. A city audit showed that Heumann had spent several thousand dollars of the fund on travel, flowers, parking tickets, dues and memberships, although the agency's board had approved none of expenditures.

Kloch said he was instructed to report only on the criminal charges, but he added that "the manner in which the . . . Investment Fund was recorded or handled may well present issues of the proper exercise of managerial discretion."

Heumann declined comment, his wife said.