A novel alfalfa variety designated 09N12CY and seed, plants and plant parts thereof. Methods for producing an alfalfa plant that comprise crossing alfalfa variety 09N12CY with another alfalfa plant. Methods for producing an alfalfa plant containing in its genetic material one or more traits introgressed into 09N12CY through backcross conversion and/or transformation, and to the alfalfa seed, plant and plant part produced thereby. Alfalfa seed, plant or plant part produced by crossing alfalfa variety 09N12CY or a trait conversion of 09N12CY with another alfalfa plant or population. Alfalfa populations derived from alfalfa variety 09N12CY, methods for producing other alfalfa populations derived from alfalfa variety 09N12CY and the alfalfa populations and their parts derived by the use of those methods.