The statement being made on stamp paper, certified, signed or witnessed does not necessarily make the statement binding. However it does show the intention of the parties to make the statement official and binding between them. The binding nature of the statement continues even if the document is not made on stamped paper. In the same way, signatures, witnesses, etc. do not actually have an effect on the binding nature of the statement.
The document can be legally binding if Section 10 of the Indian Contract Act, 1872 is complied with. A contract needs to be made by the free consent of parties competent to contract, for a lawful consideration and with a lawful object, but these conditions shall not affect any law which requires that a contract is required to be made in writing or in the presence of witnesses.
The only possibility for the statement to be declared illegal is if the purpose or the objective of the statement is illegal in any form. If the conditions given or the objective of the statement is illegal in any form then the agreement can be declared illegal by a Court. Further if the term of the agreement is impossible to perform or it is uncertain then the contract will be void and therefore it cannot be imposed.
Kindly do let us know about the contents of the written statement so that we can help you ascertain the validity and enforceability of the statement.