Depends which country this is in. The letter is in English language and uses the words "federal" and "state" so probably this is USA or Australia. Even so the wording is clearly designed to bar employees from the workplace if they decline to comply with arbitrary medical procedures so I am guessing no it is not legal. I am in England and an employer would be in a very weak position if they tried this and someone took it to court.

Also note how the letter fails to say what happens if you submit to their testing and get a positive result - do they just send you home and if so do you still get paid? Our schoolkids here were quick to understand that they could generate a fake positive result using an orange juice sample, then they all got a free couple of weeks off school. Smart employees might get the same idea.

In the real world though if it were me who received the letter I don't think I could get excited about it. Almost certain that if they really pushed it to the point where you were expected to get these tests on a regular basis and you just said no when it actually came to being tested then nobody in the admin would want the hassle and would just quietly tick the box and forget about it.