The predicative нђдо 'must, have to' is ambiguous when the negative particle не precedes: не нђдо can mean either mustn't/shouldn't or don't have to, but the usual interpretation is mustn't/shouldn't.
The unambiguous way to express don't have to is to use a form of the verb мћчь 'can, be able to' with the particle не placed before the infinitive that accompanies it: ї могџ не писђть 'I don't have to write', вІ мћжете не писђть 'you don't have to write', etc. In these constructions the infinitives are Imperfective.
In a more conversational style you can omit the words in parentheses.
Necessity: Нђдо убрђть со столђ. You have to clear off the table.
Prohibition: Не нђдо убирђть со столђ. You mustn't/shouldn't clear off the table.
No necessity: (ВІ) мћжете не убирђть со столђ. You don't have to clear off the table.
Another way of expressing no necessity is to use the predicative не обязђтельно. This is a handy way to give a short answer to a нђдо-question:
— (Нђдо) убрђть со столђ? "Do I/we have to clear off the table?"
— Нљт, не обязђтельно. "No, you/we don't. (It's not required.)"
— Нљт, (тебљ) не обязђтельно убирђть. "No, you don't have to clean up."
— Нљт, (тІ) мћжешь не убирђть. "No, you don't have to clean up."
— Дђ, обязђтельно. "Yes, you/we/someone really must."
The past tense of не нђдо is не нђдо бІло; it is just as ambiguous as не нђдо. It can mean either shouldn't have or didn't have to.
— (Тебљ) не нђдо бІло ітого дљлать. You didn't have to do that.
  or: You shouldn't have done that.