There is no religious involvement in a civil ceremony. If you go secular you create a verbal contract in response to the specific prompting of a civil administrator in the presence of your spouse ("I do" in this context is a contract), witnessed by those present and written into record by the signing of the marriage certificate. The words "I do" are the contract, not the certificate, which is proof that you said it. All of this is also true of a religious ceremony, the difference being that a priest, pastor, reverend, call him or her what you will, replaces the civil administrator and so in doing so the contract is witnessed by those present and also the particular God that you pray to.