Dealer Requesting Modification of Sale Contract

I purchased an unregistered demo vehicle with 4,000 miles on the odometer. The car is an electric vehicle. At the time of purchase, the dealership informed me the vehicle is still considered "new" and eligible for the EV tax credits. I assumed this also meant that I am eligible for the California clean vehicle rebate. However, the CA CVRP requires that the car be defined as "new" according to California Vehicle Code (CVC) Section 430. Based on the CVC Section 430, the vehicle is considered new if it is unregistered. However, the definition of used vehicles as defined in Section 665 include "unregistered vehicles regularly used or operated as demonstrators in the sales work of a dealer." When I purchased the vehicle, I signed a used vehicle disclosure form in which the car was listed as an unregistered demo vehicle. However the retail installment sale contract listed the vehicle as new which eased some of my concern as the CA CVRP requires I submit a purchase agreement with my rebate application.

More than a week after I signed the original contract, the dealership contacted me requesting a change in the contract stating that California requires the vehicle be disclosed as used so the sales contract must be modified to list the vehicle as used. I have sent emails out to the CA CVRP as well as the IRS to verify my eligibility for the CA rebates and federal tax credits. If it turns out that I don’t qualify for the rebate or tax credit and the dealership refuses to negotiate a lower price, I would like to return the car. If I refused to sign this new contract and agreed to returning the vehicle back to the dealership, am I entitled to receive a refund of my down payment? They have already cashed the check I wrote for the down payment.