Can a employer force a employee to take a health screening offered by the insurance company. The paper that I'm supposed to sign claims that I voluntarily request to participate, when in fact I do not?

Not enough info. They can force you to take a drug test ( well you do that voluntarily also) but if you don't you lose your job.

So what type of test is it,

Presumably the employer has a reason for asking you to take the screening test. Perhaps your doing so helps lower insurance rates which helps the company bottom line which, in the long run, may benefit you and your fellow employees through continued employment - not a bad thing these days.

I really don't know, and it your business, of course, but I hope you are taking the long view on this issue. If it's a free screening it doesn't seem all that bad a thing, all else being equal.

This is not a drug test, it is for cholesterol etc, blood pressure, liver health, nicotine.

If they furnish or you have health insurance and it is required for that, you can merely refuse any of the benefits, the insurance company can require them

They can require it prior to hiring you