Can my employer deny my PTO request?
In the US, yes — almost always. The Fair Labor Standards Act (FLSA) doesn't require employers to offer PTO at all, and where it's offered, employers generally control when it can be taken. Reasonable business reasons (staffing gaps, blackout periods, peak season) are valid grounds for denial, and most state laws don't override that.
What changes the calculus is the type of leave. PTO and vacation are usually employer-discretion. Sick leave protected by state or city law (California, New York, Colorado, and others) generally can't be denied if you're actually sick and you give the required notice. FMLA leave for a qualifying serious health condition or family event also can't be denied if you're eligible — though your employer can require certification.
If your request was denied for a reason that looks discriminatory (only certain employees get blackout dates, requests denied around protected medical leave) or that contradicts your written PTO policy, that's a different conversation — start with HR, then a state labor board if needed.