The 38-year-old was taken to Govan's Helen Street police station on November 16 where he spent the rest of the weekend in the cells.
Miller, from Bishopbriggs, is accused of failing to give the police two breath samples at the police station.
He also faces a charge of urinating on Woodville Street in Glasgow's Ibrox area.
Miller appeared in the dock for a pre-trial hearing yesterday at Glasgow's Justice of the Peace Courte.
He maintained his plea of not guilty and the case was continued to trial next month.