Legal Question in Sexual Harassment in New York

Re: Do I have a case without tape recorded evidence?

You might.

It all depends on what you mean by "unprofessional manner," who is willing to corroborate your story, and the circumstances of your termination.

It's illegal to discriminate agasint an employee because of gender. One manifestation of such discrimination is called "sex harassment." There are two kinds of sex harassment: (1) sex in exchange for employment ("quid pro quo"); (2) hostile environment, i.e., an environment that is offensive in a sexual sense both to the plaintiff and to the average observer. It's also illegal to retaliate against an employee for reporting incidents of discrimination.

You didn't say the supervisor demanded sex on penalty of termination, so this is not a quid pro quo situation. As to hostile environment, I don't have enough information to give you an opinion. Some thoughts -- asking an employee out on a date is not harassment. Constantly subjecting an employee to disgusting jokes and images most likely is.

As to the reasons for your termination, I would need to know all of the facts.