yes

If you live in Nevada an employer does not have to. In fact the Nevada will defend the employer, if an employee is injured on the job and the employer does not have W/C Insurance. I've been though this.

In the state of Illinois, the employer is required to carry workman's compensation.

When you intend to write a letter stating that your employer does not carry health insurance on you, you need to have all facts in place. This is an official letter and ensure that you include all your details and those of your employer for reference purposes.

That is between you and your employer.