Assuming that both you and your wife are trustees and the trust agreement/amendment(s) give each of you the power to transfer property into the trust, then either of you can sign the form. Don't need to have both signatures, just one, unless your trust specifically requires more than one trustee to sign off on transfers.
And yes, you do have to sign the form as trustee. So for example, I would sign it as "David Browne, Trustee."

