I’ve decided to keep my business open during the Coronavirus crisis. But one of my employees elected not to report for work. Am I still required to pay them?

No. For the non-exempt employee, an employer is not required to pay a non-exempt employee for the time in which he or she performs no work. 

For the exempt employee, the employer may make a deduction in pay in full-day increments pursuant to Conn. State Agencies Regs. § 31-60-14(b)(1)(B) because the employee is asking for the day off for personal reasons.