Does a contract require a signature to be legally binding in the state of Idaho .

It's not really a question of differing state law in this case, it's a question of what the contract is for.  In all states, as far as I know, only certain types of contracts are required to be in writing; most oral contracts are enforceable.  Thus, if we, both having the legal capacity to contract, neither being under duress or reasonably relying on any misrepresentations, agree that you will buy my tie for $10, an enforceable contract has been made with no writing needed. Where a contract is required to be in writing, it generally must be signed by the party against whom it is sought to be enforced, but there are exceptions, particularly where parties perform under an oral understanding for some time.  Some types of contracts require even more formality, such as witnesses.