A coalition of public employe unions in Prince George's county has agreed to stage a work-to-the-rule slowdown starting today, in an effort to force County Executive Lawrence J. Hogan to relent on his proposed budget cuts.

The work-to-the-rule job action was announced by Toby Rich, president of the Prince George's County Educators Association and co-chairman of the Public Employes Coalition, a group formed to fight the cuts.

The public employes are particularly nettled by Hogan's efforts to hold their salary increases to 3 precent, instead of the 5 percent that teachers won in a new contract and the other workers are seeking.

The job action would involve roughly 13,00 school employes and 4,300 others who work in hospitals, county offices, road projects, and other county jobs. For safety reasons, policemen and firemen are not being asked to participate.

The work-to-the-rule action, if observed, means that employes would hold strictly to their contracts, refusing to perform any extra tasks. "Everybody would work only within the exact confines of their contract, only those duties which are required of them," Rich said yesterday. "For example, a public works employe will not use vehicles or equipment that have safety violations. . . say, a cracked mirror."

Rich said the job action would continue indefinitely, until Hogan yields on his fiscal 1980 budget cuts.