Local Controller described a questionable 'Contact Approach' clearance issued when requested by the pilot and the weather conditions deteriorate to IFR.

Narrative

I was the relieving Controller on the local position. The field had just gone IFR and it was snowing. We had 2 miles ground visibility and it was decreasing. A C172 called approximately 9 miles northeast of the airport requesting to land. I told the aircraft to enter the left downwind to Runway 23 and report the mid field right downwind. I waited a minute and called the aircraft back to tell him that the field was IFR and to say intentions. He requested a Visual Approach; then corrected his request to a Contact Approach. I then asked the pilot if he was IFR rated; his response was yes. I was trying to get N90 on the line and no one was responding to me. I was discussing with colleagues whether or not I could clear the C172 for a Contact Approach or if he needed to be on an IFR flight plan and communicating with an Approach Controller. And I was trying to coordinate with N90 EWR sector; to no avail. My intention was to coordinate with N90 to have the aircraft contact them and be sequenced to the airport behind additional jet traffic. Unfortunately; I could not get N90 on the line. By the time N90 did respond the C172 was on the ground. I did not have the aircraft in sight and did not see him until he was adjacent to Taxiway F; at which time I cleared the C172 to land on Runway 23. I believe it happened for many reasons. Miscommunication and inexperience on my end and the pilot's played key roles in this event. The pilot had the current ATIS code; which described the field conditions as being IFR. The pilot should have known what that meant and what his responsibilities were. Also; the pilot; in my opinion was afraid of icing conditions developing on the aircraft was landing here no matter what. Having recently been certified; I have not been exposed to all Air Traffic situations and have never experienced a VFR aircraft in weather difficulty or a Contact Approach. Also; I was distracted because I couldn't get N90 on the line after several attempts. Recommendation; pilot awareness and knowledge on what their responsibilities are; consistent and recurrent training for Air Traffic Controllers; especially on situations that aren't frequently experienced.