The phrase "to sign the note" means to write your signature on a piece of paper, usually to indicate that you agree or promise to do something mentioned in the note. Full definition
The lender may also impose additional conditions requiring that you agree to submit to a deficiency judgment or sign a note for the deficient amount. (valuepenguin.com)
At least one owner must provide unlimited full guarantee or sign a note as a borrower. (valuepenguin.com)
Sometimes, dreams of pregnancy occur even before the earliest subtle signs noted above occur. (doctor-info.website)