Are you employing him, meaning is he on payroll, you're withholding taxes, social security/medicare, etc. and reporting his income on a W-2? Or is he engaged through a third-party agency as the employer of record? Or is he paid without any tax withholdings and you're reporting his income on a 1099?
Federal law and most state laws don't require paid time off but many employers offer it as a matter of policy. There are some states and municipalities that are starting to mandate paid time off but it's still pretty limited.
If you're engaging him as an "independent contractor" but supervising his work, providing him with the tools/equipment to get the work done, etc., then you might be misclassifying him as an independent contractor which is a different set of issues.
I don't envy small business owners. There are lots of regulations out there to keep track of and it's pretty much impossible to comply with all of them.