Chase Manhattan Corp. has joined rival Citicorp in trying to penetrate the Maryland banking market, and Chemical Bank, another New York financial services giant, served notice yesterday that it also plans to enter the competition for a share of the same out-of-state market.

Chase, which owns the second-biggest bank in New York, has applied to set up a Maryland-chartered institution in Rockville. Approval of the application would clear the way for Chase to operate a so-called limited-service bank.

Chase officials have not said whether they ever intend to operate a full-service bank in Maryland. Officials did say, however, that Chase's proposed Maryland bank would concentrate on real estate lending and middle-market commercial lending.

In the meantime, Chemical Bank, which is a unit of Chemical New York, announced yesterday that it will file an application with Maryland's banking commissioner to open a limited-service, state-chartered bank. The planned bank would provide operations and back-office support for Chemical's consumer and commercial banking business.

Under Maryland law, a limited-service bank may operate only one office in the state but may not advertise or solicit deposits from potential customers. The law is designed to prevent out-of-state banks from competing directly with Maryland banks.

The only limited-purpose bank currently operating in Maryland is Citibank Maryland, N.A., a subsidiary that Citicorp operates in Towson. Citicorp also operates its Choice credit-card division from facilities in Towson.

The Chase application was filed only a week after the announcement of an agreement between Citicorp and Maryland Gov. Harry Hughes that would allow the giant bank-holding company to operate a statewide, full-service bank.

A bill pending in the Maryland legislature would allow any limited-service bank operating in the state on July 1 to become a full-service bank. It's not clear whether Chase or Chemical could meet the July 1 cutoff date, even if their applications are approved before then.

Under a separate bill that would approve Maryland's participation in a regional banking pact, national banks outside a region including 12 southeastern states and the District of Columbia would not be permitted entry to Maryland until four years after that bill has been passed.