Try the Following Code
SELECT Closing_Date = DATEADD(MONTH, DATEDIFF(MONTH, 0, Closing_Date), 0),
Category,
COUNT(Status) TotalCount
FROM MyTable
WHERE Closing_Date >= '2012-02-01'
AND Closing_Date <= '2012-12-31'
AND Defect_Status1 IS NOT NULL
GROUP BY DATEADD(MONTH, DATEDIFF(MONTH, 0, Closing_Date), 0), Category;