Can I be charged with Obstruction of justice for refusing to answer a cop's questions?

The City's Attorney helped me tape a flyer to the inside of the elevator and I exited the building. As I walked down the steps a policemen approached me with fear in his eyes and asked "what are you doing here". I said excuse me. He replied, the burglary alarm went off, why are you here. I replied, "if you are asking did I burglarize the building, no I didn’t". He went on to say that I'm not answering his questions correctly. I thought I was because he seemed to be accusing me of having something to do with the burglary alarm going off. I became angered because as four other officers came out the station noone went into the Municipal Building to see what the matter was; they all came over to me. I thought it be wise to stop answering questions at that point and as a result of remaining silent I was arrested for OBSTRUCTION- PREVENTING POLICE OFFICERS FROM CONDUCTING AN INVESTIGATION. I was not read my Miranda Rights nor was I finger printed. There was actually no burglary-false alarm.