In general, you do not need any formal contract with candidates, but you should be sure that, one way or another, you have evidence that they acquiesce in your presenting them to employers. That evidence could be email traffic, notes in your computer system, or their sending you a current resume.
I have seen clients try to avoid paying placement fees by having candidates decide to change or withdraw your "representation" of them – after the introductions or presentations are made and the placement is likely. You should not give in to this trick. The fee arrangement is between you and the client, and the candidate is not a party to it. Candidates may have a right to withdraw consent to be presented by you in the future to clients to whom they have not already been presented or introduced, but in those cases, no earned fee is involved. This issue is an additional reason for you not to have a formal contractual relationship with the candidate that the candidate could try to "terminate."
I was not sure how you currently engage candidates in connection with fee refunds, but I hope that you do not try to charge them. Many state laws regulate employment services only if they charge fees to applicants. The applicant paid fee aspect of the industry pretty much faded away long ago, but the laws are still there, and most placement firms do not deal with them.
I think that you should also avoid having a countersigned "offer letter" with the candidate. You do not want to attach yourself to any potential or arguable liability for the client's future employment relationship with the placed candidate.
George M. Reardon Attorney and Counselor at Law 45 Briar Hollow Lane, Suite 9