My question involves criminal law for the state of: New York
My son (age 20) listed our NYC address with the NYC Probation Department and this morning 6 officers (I am assuming they were officers since not one showed ID) pushed into our apartment looking for our son (my wife opened the door and the first officer put his foot in immediately). I was not home at the time. As he was not there at that time they demanded to know where he is (we have given them this information before, orally and in writing) and proceeded to search the apartment, terrifying my wife in the extreme. They would not show her the papers that they kept referring to nor would they identify themselves other than to say that they were from the Department of Probation looking for our son, no specific reason given.

Can they just enter and search a private apartment at will after banging loudly on the door and the outside window while repeatedly ringing the buzzer and calling the home phone, without any warrant or ID? What are my options here? Is this behavior legal?

Thank you.
DS, New York City