Does An Employer Have To Cover The Cost Of An Employee's Physical That Is Required For Ongoing Employment? (new Jersey, Usa)

I work in childcare. After 2 years of my current job, I was told that I must undergo a physical exam and mantoux test. The problem is that I am currently uninsured (a physical exam can cost up to $200, about a third of my biweekly paycheck), and when I explained to my boss I wasn't insured, she told me that I would have to pay out-of-pocket, and to request payment plan from the doctor. This honestly doesn't feel right to me, especially after my cousin told me that the job has to pay for it. I would like some real advice, and would like to know if what my cousin said is true. Thanks ahead of time!