What is discrimination based on perceived sexual orientation?

Unless you are being charged with sexual misconduct, harassment, or discrimination yourself, your employer has absolutely no right to inquire about your sex life, orientation, or anything else related to personal relationships. However, if your employer is conducting an investigation and you have been identified as the subject of the investigation you should immediately consult with an employment lawyer or a criminal defense attorney based on the specific fact scenario in your case. In the latter case don't post any more specific details on a public forum such as . Speak with a lawyer in private.

Was there an adverse employment action taken against you - in other words, based on that accusation, did something bad happen to you at work? Speak to an attorney.

Your question is too vague to answer. It depends on many factors, e.g., did you have sex in the workplace? Was it with one of your co-workers or subordinates? Was it with a client? How were you punished? Generally, a NY employer cannot take an adverse employment action against someone for engaging in legal off-duty activities, which would include sex between 2 consenting adults, unless it adversely impacts the workplace in some way.