this is probably not a legal question. But tactically, and not knowing all of the facts, if you fear losing the job, go to HR and tell them you made a mistake.
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In addition to attorney Lebensbaum's suggestion, you may want to consider having your record sealed if this event was more than 5 years in the past and you don't want to have to continue dealing with the issue.
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First, I would reach out to HR and explain to them your situation. The "cover-up" is always worse than the crime, especially when the crime is a relatively innocuous misdemeanor. Second, if the misdemeanor is more than 5 years-old you can have your record sealed by simply completing certain paperwork, and sending said paperwork to the Commissioner of Probation.
I wish you the best of luck,
Anthony Rao, Esq.
The above response is NOT legal advice, and is NOT intended to be legal advice. No Attorney-Client relationship is created through the above answer, and any communication between us is not protected by attorney-client privilege.
Under Massachusetts law, there are restrictions on what an employer can ask you (and what you are required to reveal) about your criminal background. My advice would be to talk to a lawyer about the details of your situation (for example, when was your conviction, what job are you applying for, what exactly did you answer "no" to, etc.) so you can understand your rights and decide on the best course of action (not just for this job but for future jobs). All that being said, if your primary goal is to get the job rather than knowing and asserting your legal rights, then you have a non-legal judgment call to make: tell the truth about what happened and hope they understand, or say nothing and hope nothing happens. If it were me, I would do the former.