The Chesapeake and Potomac Telephone Companies reported yesterday a slight drop in 1981 profits despite a 13 percent increase in revenues.

According to its annual report, revenues for all four C&P companies totaled just over $3 billion for 1981, up from $2.7 billion in 1980. But net income fell 0.06 percent to $318,979,000, down from 1980's profits of $319,193,000.

Additionally, C&P President Robert E. Allen noted that last year the company experienced the smallest increase in a decade in the number of telephones served by C&P--less than a 1 percent increase to a total of 8.8 million telephones.

The number of long-distance calls increased 7.3 percent. Although the increase was a little larger than last year's, it was still much less than the rate of increase experienced in previous years.

The largest drop in profits came from the Maryland company, which reported a 10.8 percent decline in net income, from 1980's level of $106,658,000, to $95,109,000. The drop was the second consecutive one for the Maryland branch. C&P officials attributed the decline to soaring interest rates and sharp increases in costs--which more than offset a 10.4 percent rise in Maryland's revenues. For 1981, revenues totaled $1.06 billion, up from $965.6 million in 1980.

C&P of the District showed profits of $38.4 million, barely above 1980's level of $38.15 million. Even so, C&P officials noted that the increase represented a turnaround from 1980 when profits actually declined by 4 percent.

Revenues for the District increased by 13.8 percent, from 1980's total of $376.6 million to $428.5 million.

For C&P of Virginia, revenues increased by 15.7 percent, to $1.16 billion during 1981. Net income was $144,671,000, an 8.2 percent increase over 1980.

C&P of West Virginia reported profits of $40,787,000, for 1981, slightly above 1980's total of $40,703,000. Revenue for this company was $393.8 million in 1981, nearly a 13 percent increase from 1980's level of $347.9 million.