Is it legal for an employer to ask you to cover your head or else if you are a woman with a partially shaved head?

It all depends whether the employer clearly states their dress code guidelines in their "Employee Handbook" that you may have agreed to and signed at some point, and that it is made available to review by all employees. You will have a case in discrimination if, your hairdo is because of religious belief or national origin. Have in mind that the law gives an employer great latitude in the ways they like to run the business (many ways of defending their actions) but they cannot discriminate against an employee on the basis of their religious beliefs, national origin, race, gender, age, and in Massachusetts sexual orientation. It is always preferable to, without escalating things and causing yourself trouble to have such warnings or remarks in writing.