Are they also going to do a psychological screening? Chances are they will do a psych screening and if you have a history of any psychological disorder they will request medical records.
They will also ask if you have ever had any panic/anxiety attacks or about your last episode of depression (if that is the case).
If you medical history is clear and you do not have a history of panic/anxiety attacks, they'll ask why you take the SSRIs. Hopefully you have a good reason that won't compromise your position with the NYPD.
If you are no longer on any SSRIs and they see you previously had a script for them, again, they'll go through your medical history and ask why you were taking them.
But to answer your question, for a general drug test, they will not likely test for SSRIs unless it is suspected that you are using SSRIs without previously telling them or without a prescription.