I work for a local municipality. I drive a city vehicle (assigned to me) daily as part of my job. The vehicle is parked several miles from my office.
Questions: When I drive my POV from my office to the storage lot, is this mileage reimburseable? If I am involved in an accident during the drive in my POV, does Workers Comp apply, or just my private vehicle insurance?

Whether you are reimbursed mileage at all it up to the municipality where you work. Whether WC applies or not depends on the exact circumstances under which you are injured so there isn't a one size fits all answer. Were you actually injured or is this hypothetical?

Injury /accident is hypothetical. If I WERE in an accident and fault was not determined, I would guess that I would be sued in Civil, but the City has deeper pockets, so they would also be named.
The City does have a policy in place that allows for City employees WITH access to vehicles to be reimbursed for mileage if they choose to drive POV.

who can be sued also depends on a great many factors that can't really be fully explained in a hypothetical situation. Also, who is named in a suit and who is sucessful and ultimately pays up are very different things.

I'm confused. If you're driving a city vehicle, what expenses do you personally incur that would need reimbursement?

I report to work at my office in my POV. My City vehicle is stored in a gated lot several miles away. When I need to use my City vehicle, which has equipment in it which is required to do my job, I must travel the three miles in my POV to retrieve my City vehicle. Are the three miles (6 miles rountrip) reimburseable? The City does have a Reimburseable Mileage Policy in place.

Then they should follow their policy. I have no idea if there are any restrictions in the policy. There is no LAW in Texas requiring reimbursement of business expenses incurred by the employee.