What is the ruling of Islamic law regarding a marriage contract that was verbally concluded between a male cousin (son of the maternal aunt or paternal aunt) and a female cousin (daughter of the maternal aunt or paternal aunt) without official documentation? Is this considered merely an engagement? And what should the girl tell a new suitor about what happened?

If the proposal and acceptance were exchanged between your brother and your maternal cousin in the presence of two witnesses, then the contract is valid, and you become his wife. The writing or documentation of the contract does not prevent its validity. Marriage in Islamic Sharia (definition) is a verbal contract that takes place by uttering the proposal and acceptance in a single session with words indicative of them, by those who are legally competent to contract, in the presence of two adult, sane, Muslim witnesses who hear and understand the proposal and acceptance. Documentation is a matter mandated by law to preserve the contract from denial. It is not permissible for you to marry anyone else except by divorce or annulment. If your maternal cousin does not divorce you or agree to a khul', then refer the matter to the judiciary. If the judge rules for divorce or annulment, then it becomes permissible for you to marry someone else.