One school may have to take on half of its staff before being told the teachers' names and ages, or learning anything about their current schools or medical histories. Many others will have to take on a quarter of their staff on this basis.
The governing bodies say that Bradford council has used bullying tactics to make sure that schools accept their share of re-deployed teachers - the result of the West Yorkshire city's decision to abolish its middle-school system.
John Patterson, head of Bingley Grammar, a grant-maintained school, said:
"GM schools are committed to the principle of appointing staff from the closing middle schools. However, we are unhappy about being forced to appoint staff without being able to meet them, and without staff being able to exercise any real choice where they end up.
"Considerable pressure has been brought to bear upon staff and governors to sign the agreement, and the pressure has been of an extremely threatening nature."
Joan Law, headteacher of Laisterdyke GM middle school, has not signed the agreement. She said that if the proposed changes were to go ahead, the size of her school would double and her governing body would have to take on the staff without knowing who they are.
The Department for Education and Employment has been asked to rule whether the Bradford arrangements are legal.
Diana Cavanagh, Bradford's director of education, said the staff-placement scheme had been agreed with the teaching unions, the Church of England diocese and the Funding Agency for Schools.
Only three local authority schools have not signed the agreement.
The teacher unions say the arrangement is fair. Bev Marshall, a National Union of Teachers' regional official, said: "The alternative would be for everybody to have to apply for their jobs again.
"As there are still the same amount of pupils, nobody should need to lose their job."