The Labor Department will investigate charges by the NAACP that New York City and possibly other local governments have diverted federal funds for public service jobs to other programs, according to a department spokesman.

The allegation that New York has improperly used federal jobs funds for other purposes came in a letter to Labor Secretary Ray Marshall from Herbert Hill, national labor director of the NAACP.

In the letter, which was written Feb. 23 and released yesterday by Hill, the NAACP official charged that funds allocated for wages and job-related benefits under the Comprehensive Employment and Training Act (CETA) "are being transferred to a variety of municipal agencies in violation of the expenditure control and reporting requirements" of the act.

The problems are "not unique to New York" and "exist in many other communities," Hill asserted, adding that they are largely "a consequence of the lack of adequate monitoring and accountability procedures by government agencies that characterize federally funded training programs."

CETA currently provides funds for up to 310,000 jobs for the unemployed on local government projects, and the Carter administration is proposing to expand the program to 725,000 jobs over the next 18 months.

Congressional critics have questioned whether these represent new jobs in all cases, but New York has never before been charged with diverting funds and has not done so, said Deputy Mayor Lucille Rose, who is also the city's labor commissioner. "We haven't done anything other than the federal government requires," said Rose.

Hill, in a telephone interview, said he had documents indicating that city officials were aware they were using CETA funds for purposes not prescribed by the law. "They were warning each other of the risks," he said, "but they weren't saying, 'Stop doing it.'" A Labor Department spokesman said a "thorough investigation" of the charges would be conducted by the department's New York regional office, as prescribed by CETA legislation.