Criterion Insurance Co. yesterday reported a sharp improvement in profitability for the third quarter and first nine months of 1977.

The auto insurance firm, which is an affiliate of Government Employees Insurance Co. reported third-quarter earnings of $2.29 million ($1.57 a share compared with $745,000) (51 cents) for the same period last year.

Included in the recent earnings was a one-time gain of $834,000 (57 cents) from utilization of a tax loss carryforward credit plus operating profits of $1.46 million.

In the first nine months, Criterion earned $6.7 million ($4.60 a share) vs. a loss of $4.1 million in the comparable 1976 quarters.

Chairman Alvin E. Kraus and president George F. Lewin told stockholders, in a message now being mailed, that the company had an underwriting profit in auto insurance of $2.8 million for the first three quarters of the year compared with an underwriting loss of $7.6 million a year earlier.

They credited rate increases and lower claim frequency as major factors in the improvement, despite large average claim payments. Now policies sold increased 28 per cent in the first nine months compared with last year although the company has stopped writing new policies in South Carolina, where a rate increase was denied.

Tesdata Systems Corp., of McLean, reported earnings for the first nine months of $1.17 million ($1.01 a share), up 21 per cent from $968,000 in the same period last year, when per-share profits were $1.04 because of fewer shares then outstanding.

Sales of the company, which produces systems to monitor computer efficiency increased to $9.9 million.