If a state employee has been assigned a vehicle, are they allowed personal use of it?
No. Drivers are only allowed to use state-owned and rental vehicles only to conduct official state business. Personal use of a state-owned or rental vehicle for social, recreational, religious, educational or any other purpose, whether on duty or off, is not permitted. Transportation of passengers, including state employees, is not permitted, unless this transportation is necessary to perform official state business. For appointed officials, see the Connecticut Handbook for Appointed Officials.
With that being said, there are several agencies that operate on a 24 hour a day / 7 day a week schedule, and would generally explain why they are in use beyond what most would consider normal business hours.
Social Service agencies such as The Department of Children and Families would often be transporting children in their vehicles. The Department of Developmental Services will often have clients during these times and may be observed at grocery stores or shopping malls as they assist their clients with the development of life skills.
Appropriate use of state-owned and rental vehicles is outlined in DAS General Letter #115 (PDF).