My employer notified me that they decided not to open for business today, when I was scheduled to work. Are they still required to pay me?

If you are a non-exempt “hourly” employee, no. An employer is not required to pay a non-exempt employee for the time in which he or she performs no work. 

If you are an exempt employee and you have worked for any portion of the week, yes. The employer is required to pay you the full weekly salary if you work for any portion of the week. 

Also, it is not permissible for the employer to make any deduction for the time that the exempt employee is absent from work from the employee’s accrued Paid Time Off (“PTO”) benefits, because Conn. State Agencies Regs. § 31-60-14(b)(2)(A) does not permit a deduction “of any kind” when a lack of work is occasioned by the operating requirements of the employer.