Yes.
You can leave a handgun in the car LOADED if you'd like.
No locked case required. CT does not have any transport or storage requirements other than that a long gun can't be loaded while you are driving the car.
Seriously, None.
I'm never in favor of storing a firearm in your car, just for ethical reasons. But if you take the proper precautions, you will be fine. I'm talking ethics now, not legalities. If you ahve a car with a trunk, disable the remote trunk release and seat fold down release and store it there. From a legal perspective, you could leave it out on the passenger seat and be in compliance with all laws.
Don