Yes, as to your first question and No as to your second question. To follow-up on the comments from the previous Expert, given that it appears you are a non-resident of MA, you are not required to file, nor should you file a MA return. The situation might be different had you been a resident of MA but were given the option to work remotely in another State, such as TX. Your employer may be withholding MA taxes because that is their default option for all employees. What you could do is inform your Human Resources department (or whichever department in your company handles matters of this type) and request that they stop withholding for MA as you are not a resident of that State.
To the extent your employer withholds wages for MA, you will need to file a MA return to obtain all of that withholding. The fact that your company is a public institution is not relevant on the issue of whether you should be paying taxes to MA. What is relevant regarding MA and State taxes is whether you are a resident of MA. Because you are not a resident of MA, there is no tax obligation owed to MA.
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