American Telephone & Telegraph Co.'s equipment division is getting a divorce from Chesapeake & Potomac Telephone Co.

The C&P telephone companies that serve customers in the District of Columbia, Maryland, Virginia and West Virginia no longer will bill their customers for the phones they rent from AT&T.

In fact, customers can look forward to three monthly bills or more if they use a long-distance competitor's service -- one bill from C&P which includes local calls and long-distance calls placed with AT&T, one bill from AT&T Information Systems for their rented phones, and one or more bills from the non-AT&T long-distance company.

"For a lot of those people out there that haven't paid attention to divestiture, the fact is that customers who lease telephones will be getting a separate bill from us starting the first of the month," said Al Wann, a spokesman for AT&T Information Systems, the equipment arm of AT&T. Under the terms of the breakup of the Bell System Jan. 1, 1984, AT&T Information Systems must bill for the rented phones themselves.

Customers were notified by C&P about the new billing on their last bill, said Wann. "The charges are not new -- they are just separated out. So the total for the monthly payment will not change," he said.

Customers who lease one or two phones from AT&T will be billed quarterly; customers leasing three or more phones or paying monthly bills of $12 or more will receive a monthly bill, and business customers with multiple lines will also get a monthly bill, he said.

The billing transition began last spring on the West Coast and the whole cycle will be completed by July. AT&T has plans to begin billing for WATS and 800 service separately from the local phone company's bills later this year and is testing direct billing for AT&T long-distance service, said Wann.

In areas where C&P now offers customers the "equal access" option that allows users to reach long-distance companies other than AT&T without dialing lengthy codes, the C&P companies plan to handle billing. That includes billing for GTE/Sprint, ITT, AT&T, and MCI Communications Corp, said C&P spokesman Mike Houghton.

The billing will only be handled, however, if these companies remain "secondary" long-distance companies or companies still reached through dialing the lengthy codes, he said. If these companies are chosen as "primary" long-distance service companies, customers will receive a separate bill from them.

But customers who do not pay their long-distance bills, beware. "We have the ability to deny local service if the total telephone service charges are not paid," said Houghton of C&P. Customers would get a notification before service was disconnected, he said.