There are several places to find this information:
If you have access to the original muster rolls (on microfilm), you can look though each one of them and see the original information. The microfilms for Missouri units are held at the Missouri State Archives at Jefferson City. If you are not familiar with working with these Muster Roll microfilms, I do not recommend using them. They are hard to read, some missing and sometimes in illogical order. The only redeeming factor is that it is the original information that all the other sources copied from.
If you have a large library or college nearby, they might have the Supplement to the ‘Official Records’. This is the second set of books published by the government. They have all the various Regiments Event Records from all over the country (Both USA and CSA). Just find the Regiment you want and they are listed by Field and Staff and then each Company. This is the preferred method of reading the Event Records.
If you have access to the Compiled Service Records microfilms, the Event Records are at the start of each Regiments soldier’s records. These microfilms are available from NARA (for a price) or available for viewing at the Missouri State Historical Society at Columbia, MO. (I think a library in St. Charles has copies, but I am not sure.)
NARA also published a microfilm that just has the Event Records on them.
I am sure an on-line service (like listed at the top of this web site) can obtain copies of the Event Records if you do not have easy access. You can get the Compiled Service Record and Pension file at the same time from places like that.
You will want to be sure and read both the Field and Staff and the particular Company Event Records as they each have a little different information. Other Company Event Records also come in handy as they might mention other Companies that they were with during that time period.
Some research will turn up a couple of other ways to find them, but these are the most forward.
Hope it helps.
Craig