Can You Say Need Not?

You can ALWAYS say "not need to", but you can only say "need not to" in specific cases.

Is need not grammatically correct?

Generally "need not" is less personal and has less to do with the noun "need" than "don't need to". "You needn't be overly concerned" means "It is of no use for you to be overly concerned." The use of modal "need not" makes it clear that the sentence is not about your needs or even about whether something is necessary.

Can we use need not?

Need not can be contracted to needn't. We don't use don't/doesn't/didn't with the semi-modal verb need: You need not spend a lot of money on presents. (formal) (or You needn't spend a lot of money on presents.)