The Chesapeake & Potomac Telephone Co. of Maryland is offering a new service that will allow customers to automatically connect a call after getting the number from directory assistance. The cost is 30 cents, besides possible fees for directory assistance.

Residential users are allowed 12 free directory calls a month. After that amount, the charge is 25 cents a call. For disabled customers who can't use a directory, there is no fee if they notify C&P; of their disability.

The new service, called Connect ReQuest, became available to about 30,000 Baltimore downtown customers through 22 telephone exchanges yesterday. The coverage of Connect ReQuest will gradually expand and will cover the state by the end of 1992, a C&P; spokeswoman said.

Under Connect ReQuest, customers calling 411 asks for assistance in obtaining a number. Then a recording informs the customer they can connect with the number automatically by pressing a certain button on their touch-tone phone.

The service is not available for those with rotary-dial phones.