The right way to do this (avoiding all the year/month date-part manipulation in the process) in all cases is to use what some people call a "Closed-Open Interval" or "Half Open Interval" where the start date is inclusive and the end date is exclusive. The generally accepted standard is to do something like this for your reporting queries.

SELECT columnlist

FROM dbo.YourTable

WHERE SomeDateTimeColumn >= DATEADD(mm,DATEDIFF(mm,0,CURRENT_TIMESTAMP),-1) --Beginning of previous month (inclusive)

AND SomeDateTimeColumn < DATEADD(mm,DATEDIFF(mm,0,CURRENT_TIMESTAMP), 0) --Beginning of current month (exclusive)

;

The code above will always return the previous month's data based on whatever the current date is even when the year changes.

The short explanation of the code is that the "0's" are shorthand for '1900-01-01' (base date) and "-1" is shorthand for '1899-12-31'. The DATEDIFFs count the number of monthly boundaries crossed since the base date and the DATEADDs convert that count of boundaries back to a date which will always be the first of the month for whatever month is returned. It won't work for dates before 1900 but it will work for all dates from 1900-01-01 thru 9999-12-31.