State laws vary but in general if your project car has been registered it will be required to have auto insurance in the state minimum requirements on it at least. There are some states where you can get your car placed into a non-operable registration category from the Department of Motor Vehicles (DMV) and thus can take off insurance until the car is drivable and will be operated on the streets again.
For example, California car insurance law doesn't require all types of vehicles to have insurance. These include off-road vehicles, trailers, special equipment vehicles, and those registered as PNO (planned non-operation). California defines non-operational to mean that the vehicle will not be driven, towed, stored or parked on public roads or highways for the entire registration period. This state allows its residents to file a notice of non-operation to save on registration fees and insurance costs for a vehicle that is not being driven.
The CA DMV states that if it is time to renew the registration for a vehicle that you do not plan to use, you may place your vehicle on Planned Non-Operation (PNO) status. With a car that is listed as a PNO you cannot drive the vehicle legally and it cannot be parked on a public street. If you to drive the car under PNO, you will need to register it. So if you plan on working on your project car when you get to the point where you will need to test drive it and drive it away from where you have it stored or garaged then you will need to take the PNO off and thus register and insure the car so that it is back on the road legally.
In CA a planned non-operation (PNO) fee is paid to the DMV instead of the regular registration cost, the non-operational status will remain until you decide to operate the vehicle and pay full registration renewal fees and place insurance back on the vehicle.
Kansas is another state with laws that allow you to take insurance off of a car that is not being used but they have you go about it in a different manner. As long as a vehicle is titled to be operated on Kansas roads, it must be covered by an insurance policy that meets the minimum liability requirements. This applies whether the vehicle can be driven or whether you simply make a personal decision to not drive it for a period of time.
However the Titles and Registrations Bureau at the Department of Revenue for KS allows you to change the title to "non-road use" status under certain circumstances. If you do so you will not have to insure the vehicle until it is to be driven. When you are ready to operate the vehicle again, it will need to pass a Kansas Highway Patrol inspection before you will be allowed to re-title it for road use. When the vehicle is to be driven again, you must have it insured immediately upon being re-titled.
To find out about what your state laws are and if they allow you to take insurance off of a car that is not being driven contact your local DMV. They can tell you if there is any special title or registration category that you can place your project car under while you are working on it and it is not operational. If there is find out when you can take insurance off of the vehicle and when you must place it back on so that you will not be penalized by the state for just taking insurance off of a vehicle and having a lapse in the eyes of state laws.