Can a bank refuse to lend if the seller is also taking back a note?

Yes. A bank is not obligated to lend on any particular financing structure, and lenders routinely have views about how much seller financing they are comfortable seeing behind their own loan. A vendor take-back note changes the buyer's overall leverage and the pool of assets available to secure the bank's own position, so a bank assessing an acquisition loan will often ask about any vendor take-back as a matter of course, not as an afterthought.

A bank uncomfortable with the arrangement might refuse to lend altogether, or more commonly, condition its financing on changes such as subordinating the vendor take-back behind the bank's own security, capping the size of the seller-financed portion relative to the total price, or requiring specific terms on the note itself. None of this is dictated by law; it reflects the bank's own credit policy and risk appetite for that particular deal. A buyer planning to combine bank financing with a vendor take-back should raise the arrangement with the bank early, rather than presenting it as a finished plan once the seller's terms are already locked in.