Chesapeake & Potomac Telephone Co. asked yesterday for a 27 percent rise in telephone rates for Maryland residents, less than four months after it received permission to raise rates by more than 13 percent.

If accepted by Maryland utility commissioners, the increase would push the cost of pay-telephone calls from 15 cents to 25 cents, the highest in the metropolitan area.

Residents would see a $2.60 to $3.40 increase in their monthly phone bills.

Installation costs also would rise--by 23 percent or more in some cases--under a new pricing formula C&P wants to impose.

The rate request, contained in a petition before the Maryland Public Service Commission, seeks a total of $165 million a year in additional revenue.

C&P said the increase was needed to help the company finance a construction program that will total more than $356 million in 1982.

Overall, the increase would give C&P a higher rate of return than the company is now allowed, going from 11.7 percent to 14.2 percent to reflect the higher cost of borrowing money, C&P said.

Noting that the $95.3 million increase it received in March from the Public Service Commission was less than half the $202 million the company had requested, C&P's Maryland vice president, J. Henry Butta, said the additional sum was needed to meet the company's rising costs.

Last March the PSC turned down some of the proposals C&P made yesterday, including its request to boost pay-telephone calls by 10 cents.

Commission Chairman Frank O. Heintz declined to comment on the specific rate request.

Meanwhile, the Maryland Office of People's Counsel, which has fought C&P's proposed rate increases successfully in the past, criticized the latest round. "C&P can expect to lose again," said Gregory Carmean, assistant people's counsel.

However C&P spokesman Web Chamberlin said, "Hopefully, we can tell a good story in our testimony to make them understand why we still need more money."

Specifically, C&P is asking for:

* An average 27 percent statewide increase in the basic monthly telephone rate.

For Silver Spring, Rockville and Kensington residents, for example, the flat-rate service allowing unlimited local calls would increase from $12.60 to $16 a month. Message-rate service, which permits 65 local calls a month, with an additional 9-cent charge for each extra call, would rise from $9.70 to $12.30. Additonally, message-unit charges would increase from 9 to 10 cents a call.

Business customers in those areas would see their monthly rates increase from $9.50 to $11.65 per line. Exact increases depend on the type of service, the number of phones each customer has and the jurisdiction.

* A 66 percent increase in coin telephone fees from 15 to 25 cents--the first increase in local coin telephone rates in more than five years. C&P said this boost will not hurt low-income customers but rather travelers and business people, who are the primary users of pay telephones.

* A new formula for installation charges to reflect a recent ruling by the Federal Communications Commission to bring installation charges closer to their real costs. Under C&P's formula, a customer wanting to install a single phone in a new house will pay about $67 for installation compared to today's cost of $54.60.

* A new 30-cent service charge for operator verification of an apparently busy line, plus an additonal charge of 50 cents for interrupting a call. No charge would be imposed if the line was found to be out of order.