The Labor Department has its own labor problems these days, according to the union representing its 4,500 employes. But in the true spirit of labor-management disagreement, the department does not believe there is a problem.

The American Federation of Government Employees' Local 12 is asking the department's inspector general, J. Brian Hyland, to investigate whether the department's management is willfully pressing frivolous disciplinary charges against its employes.

Union president Michael Urquhart said the AFGE has been forced to seek arbitration in 26 personnel cases in the last nine months, far more than usual. He said the AFGE's request to Hyland was prompted by three recent cases, including an attempted disciplinary action against a union steward. An arbitrator overturned the action, saying the department should not have initiated the case.

Urquhart said the volume of cases places a financial burden on the union because, although the department pays for the first 10 arbitration cases each year, the union shares the cost of arbitrating the rest. Costs have ranged from about $1,800 to $10,000 for each case, he said. "They could attempt to break the union financially by these ridiculous cases," he said.

Employe grievances have increased substantially in the last year, Urquhart said, because of growing numbers of negative performance evaluations.

A department spokesman familiar with in-house labor relations, who asked not to be identified, said, "The department would disagree with Mr. Urquhart's charges. Obviously, Mr. Urquhart is free to go to the IG." He said that only about 12 of the 26 cases cited by Urquhart have reached arbitration, and that the others may be settled by negotiation. The department may end up with no more arbitration cases than in previous years, he said. CRIME RATE DOWN . . .

Whether or not Labor has labor troubles, it no longer has much of a crime problem, the department said. The latest internal security report on its Frances Perkins Building headquarters said reported crimes decreased from 200 incidents in fiscal 1982 to 138 in 1983 to 88 last year. Thefts of government property during that time decreased from more than 100 to 24 last year; there were none in the first five months of fiscal 1985.

The agency credited tighter security regulations, closer tabs on inventory and room keys, and stricter screening of security guards. The report said security costs fell after the department took over security from the General Services Administration. MINE SAFETY PROPOSAL . . .

The Mine Safety and Health Administration is considering new regulations to target companies that are repeat offenders of safety standards. The rules would subject mines with a "pattern of violations" to stronger sanctions.

Greater public attention has been focused on mine safety since a coal mine fire last December killed 27 people at Emery Mining Co. in Utah, but the new rules had been in the works for five years. The 1977 Mine Act authorized the MSHA to notify persistent violators, and, within 90 days, to reinspect the mine and shut it down immediately if violations persist. The MSHA will receive comments until April 17 on new rules, published Feb. 8 in the Federal Register.