The price D.C. residents pay for unlimited local telephone service would more than triple under the new rate increase proposal that Chesapeake and Potomac Telephone Co. has filed with the Public Service Commission.

The charge for connecting service at a new address would skyrocket from $9 to $72, while the cost of calling in a company repairman to fix a phone or install new equipment would jump to $21 for the first 15 minutes of work and $11 for each additional quarter hour. Currently, house calls cost no more than $9.

None of these increases, or others proposed in the request filed March 15, can take effect without approval from the PSC, which could take more than a year to make a decision.

But the proposal already is drawing fire from city residents, said Brian Lederer, the city's People's Counsel, who represents consumers in rate cases before the PSC. He said consumers are "agitated, concerned, angry" and seeking ways to fight the rate proposal. "There has been more community interest in this case than in any I can remember since taking this job," said Lederer, who was named to the post six years ago.

C&P Vice President Delano E. Lewis, who manages the District of Columbia telephone operation, agreed that the proposed rate hikes are steep.

"They are shocking, no question about it," Lewis said. "But we can't keep rates as low as they have been in the past . . . because as a result of competition in long distance and telephone equipment markets, prices for local service are being driven toward cost; therefore, the basic rates for local service will increase."

For the residential customer now using D.C. service, which provides unlimited calling within the District, the price would jump 224 percent--from $4.51 a month to $14.59 if the C&P rates are approved.

The bill for the metropolitan flat service, which provides unlimited calling within the metropolitan area, would increase 105 percent, from $8.83 to $18.06 a month. The measured area rate, which provides 60 calls within the metropolitan area, would increase 106 percent, from $4.51 a month to $9.28. And the economy rate, which provides a dial tone only and charges for each call, would increase 64 percent, from $2.20 a month to $3.61 a month. Those prices are for dial tone and usage for dial service; Touch-Tone service is extra. A charge also is added to the monthly bill for telephone equipment a customer leases from C&P.

C&P also proposes a fifth type of service--the controversial Optional Measured Service, which would be tied to the number of calls the customer makes each month, the distance, duration and time of day.

The basic monthly charge for OMS would be $9.28 and would include a call allowance of $2.94.

If the OMS customer used more than $2.94 in calls, he would pay extra.

C&P proposes to charge 3.1 cents for the first minute of each call within D.C. and 0.9 cents for each additional minute.

The charge would be 3.7 cents for the first minute of each local call to suburban Maryland or Northern Virginia and 1.1 cents for each additional minute. OMS users would get a discount of 60 percent on calls made at night, on weekends and holidays.

The telephone company has also asked to increase the cost of a coin telephone call from 15 cents to 25 cents--a jump of 67 percent--and to raise the rates for operator assistance for local calls.

The proposed rate changes are aimed at bringing in an additional $82 million a year in revenue for C&P, which said it had annual revenues of about $250 million in 1982. About $48 million of the 1982 revenues came from residential customers; the balance was from business and government customers.

Lewis said that government-ordered reorganization of the telephone industry has eliminated subsidies that C&P received from long-distance revenues and was using to keep local service rates low.

Without those subsidies, local rates for the company's 308,000 D.C. customers must increase, Lewis said.

C&P, which has an authorized rate of return of 12.15 percent on its investment, is seeking a return of 13.59 percent.

Lederer said residents are "particularly agitated by the local long-distance proposal OMS ; they are not amused by this advertising campaign of the company promoting OMS and they are not amused by the survey that C&P is conducting." The telephone company has spent $180,000 on an advertising campaign promoting the OMS concept. C&P also asked local residents to respond to bill stuffer surveys, indicating whether they want OMS. Lewis said that OMS was devised to enable customers to control their monthly telephone bills. With OMS, he said, customers "pay only for the amount of local service they use."