WASHINGTON (AP) _ A second New York thermometer factory has been cited for health and safety violations following a federal agency's internal investigation into questionable handling of cases by one of its own offices.

The Occupational Safety and Health Administration proposed $21,590 in fines Thursday for 22 violations at the Ever Ready Thermometer Co. of New York City, including exposure of workers to unacceptable levels of mercury.

OSHA said it inspected the company after its investigation revealed that a previous case against the company was closed by an OSHA office in New York in 1982, without evidence in the files that the violations had been corrected.

It was the second questionable case handled by that particular OSHA office.

Two weeks ago, Pymm Thermometer Co. Inc., also of New York, was fined $30,000 for 16 violations, with the agency saying dozens of workers may have been routinely exposed to toxic levels of mercury.

Pymm was cited in 1981 for allowing workers to be overexposed to mercury. The OSHA office granted Pymm three one-year extensions of the deadline for correcting the violations without requiring the company to show progress in reducing mercury exposures, according to Patrick Tyson, OSHA's acting director.

Robert Abrams, the New York state attorney general, said he has begun a criminal misconduct investigation into Pymm and its officials.

In the Ever Ready case, OSHA issued a ''willful'' citation for excessive mercury exposure, according to Chriss Winston, an agency spokeswoman. A willful violation is one in which the employer knows about the hazardous condition and has made ''no reasonable effort to eliminate it,'' she said.

Ms. Winston said mercury was found on the surface of a drinking fountain and a refrigerator, and an eating area was contaminated.

The other citations involved failure to provide protective equipment for employees, failure to provide eyewash emergency shower facilities for exposure to acids, and for electrical hazards and poor storage and handling of flammable liquids, she said.

The company has 15 days to appeal the proposed penalties to the independent Occupational Safety and Health Review Commission.

Reporters' telephone calls to the company were answered by a machine which said the office was closed.

OSHA has reassigned two top officials from the Church Street office in New York to another office in the city while the investigation is under way.