The FBI is looking into allegations of bank fraud and embezzlement against officers of a Maryland bank that has 21 branches in Prince George's and Montgomery counties, a bureau spokesman said yesterday.

Management of People's Security Bank called in the agency Jan. 20, according to the FBI office in Baltimore. Spokesman Andrew Manning would not say how much money was involved or how many officers the agency was looking at.

He did say that problems the agency would possibly look into include overdrafts improperly approved for certain customers and unauthorized loans made by the officers. He would not say whether the officers acted together.

"We haven't been in there very long," Manning said.

The investigation follows the recent resignations of two branch managers, according to bank officials, who would not tie the resignations to the FBI investigation.

Peoples Security Bank was organized in 1977 to succeed Peoples National Bank of Maryland, which was started in 1963. The bank employs 243 persons and had deposits of $187 million and assets of $207 million in 1980, according to Moody's Bank and Finance Manual, a national reference book.

Headquartered in Landover, it is one of suburban Maryland's smaller banks in terms of assets and focuses mainly on retail banking services to individual customers.