There is no requirement in law that employers offer vacations, either paid or unpaid, to their employees. Nevertheless, it is standard practice in Connecticut for employers to have some policy for paid vacations. Connecticut law requires employers to notify employees of the organization's policy on vacations and to compute withholding taxes separately when paying employees both wages and vacation pay on the same day.
Employers are required to make available to employees, either individually or through posted notice, a statement of the organization's policy on vacations and of any changes made to that policy (CT Gen. Stat. Sec. 31-71f(2)). Note that such statements have been interpreted as implied contracts that are enforceable by the state. This means that if you do not intend to pay accrued but unused vacation to employees who terminate, you should very clearly say so ahead of time in the employee handbook and in company policies.