In Maryland, as in most other states, it is the owner of the vehicle who is ultimately liable for any physical or property damage that occurs while the vehicle is being operated. The auto insurance policy also needs to have the owner of the car listed on the policy in order for it to be valid.
If you gave your vehicle to your ex but you are still on the title and the insurance is still in your name you need to take some steps to rectify this situation. You don't want to be held liable if they cause an accident and the injured party and/or their insurance company decides to come after you because you're the owner.
You want to transfer the title out of your name and into the name of your ex. This will make them the owner of the car, not you, and liable for any at fault accidents that occur in it. They will also be responsible for paying the car tabs and meeting emissions checking requirements.
Once the vehicle is in their name they need to shop around and find an insurance company. They will be the named insured on the policy. Once this is done you should cancel your insurance policy on the car. Auto insurance policies can't be transferred between people so it isn't an option to transfer the existing policy to your ex.