A federal appeals board has upheld the procedure used by the D.C. public schools system last year to lay off 571 teachers, but decided that 17 of the discharged teachers should be rehired.

The Merit Systems Protection Board, which under the city's limited home rule arrangement with the federal government still decides personnel disputes for some city employes, rejected the contention of the Washington Teachers Union that the teacher layoffs were handled improperly.

However, the board did order the school system to notify 17 laid-off prekindergarten teachers who also were licensed to teach kindergarten that they may have had a right to be reassigned to teach kindergarten.

The board's decision is schedulted to become final on July 6, unless either the school system or the teachers union appeals for review. After the ruling becomes final, the only recourse is apeal to the D.C. Superior Court.

In an appeal filed on behalf of 75 laid-off teachers, the union had charged that the school system violated a number of procedures and requirements in carrying out the reduction-in-force. It was prompted by the city's severe budget crisis in which the school system had faced a $23 million shortfall in fiscal 1980, which ended October 1. But in each case, except those of the teachers the board said should have been offered the kindergarten jobs, the board sided with the school system.

The union had charged that the schools did not set up a proper list by seniority and work performance to determine which teachers should be laid off first, but the board ruled that the school system met that requirement.

The board found that the school system acted properly in offering the laid-off teachers other positions as they opened up, although it noted that the process "resulted in confusion" on the part of many workers.

The union also contended that the schools did not take "very good" performance ratings into account when making the layoffs, but the board ruled there was no obligation to do so. The union claimed that the school system eliminated more jobs than were required by budget cuts, but the board also rejected that argument.

The union argued that the schools should have made cuts in other areas before laying off teachers, but the board ruled that the school administration has the authority "to determine what areas to reduce when faced with budget cuts."