We report results from TeV gamma-ray observations of the microquasar Cygnus X-3. The observations were made with the Very Energetic Radiation Imaging Telescope Array System (VERITAS) over a time period from 2007 June 11 to 2011 November 28. VERITAS i
s most sensitive to gamma rays at energies between 85 GeV to 30 TeV. The effective exposure time amounts to a total of about 44 hours, with the observations covering six distinct radio/X-ray states of the object. No significant TeV gamma-ray emission was detected in any of the states, nor with all observations combined. The lack of a positive signal, especially in the states where GeV gamma rays were detected, places constraints on TeV gamma-ray production in Cygnus X-3. We discuss the implications of the results.
