TSQL - Monthly Script

I need to run a script on a monthly basis (e.g at midnight on the last day of the month) which selects all the records from that calendar month. I have the below so far however as each month has a different number of days in it this will not work well. Are there any date/time criteria I can use in my tsql statement which will only select records from that month no matter how many days are in the month? I obviously need to move away from manually updating the script each month depending upon how many days are in the month!  

SELECT     *
FROM         UserLog
where logtime >= (getdate() - 30)
order by logtime asc

cheers

marco