Can a buyer require me to certify I'm not a non-resident before closing, and what if I refuse?

Yes, and most buyers' lawyers will insist on exactly this, because of the withholding obligations that apply when purchasing from a non-resident seller. If a seller won't confirm their residency status, the buyer has no reliable way to know whether it needs to withhold and remit part of the purchase price to the CRA, and getting that wrong can leave the buyer personally on the hook for the seller's unpaid Canadian tax. A residency certification, or a requirement that the seller instead produce a valid CRA clearance certificate, is a standard and entirely reasonable protective closing condition, not an unusual demand.

If you refuse to certify your residency, a prudent buyer will generally respond by treating you as though you might be a non-resident for protective purposes: withholding the relevant portion of the purchase price and remitting it to the CRA, or insisting on an escrow holdback until the position is sorted out, rather than closing without any protection at all. This can mean you don't receive full payment at closing, even if you are in fact a Canadian resident.

If you are a Canadian resident, simply confirming that in writing is the straightforward way to avoid an unnecessary holdback delaying your proceeds.