No-fault in Kentucky, as in many other states, is in reference to bodily injuries sustained in an accident, not property damage that a car received.
Under the KY no-fault insurance system, you are required to purchase personal injury protection (PIP) coverage that helps pay the cost of injuries regardless of who was at fault in the accident. If you choose the no fault option, basic KY PIP coverage is $10,000 for medical expenses, loss of income or services, and funeral expenses.
For damages to your vehicle if no citations were given and each driver feels the other was at fault then they each can place claims against the other's insurance policy. The insurance companies involved will then investigate and determine fault and if the claims will be accepted.
For a person to be found at fault for an accident there does not necessarily need to be a ticket issued by the responding officer or even if a citation is handed out to a driver an insurance company may differ in their opinion of who the at fault driver was in the accident. So after there is an investigation by the insurers of the incident they will make their own determinations of fault and decide if claims will be accepted or denied based on what they find the liability of their policyholder to be in the accident.