Celinda,
You do not say why you believe it was *your* James Thomas who had this particular service. How exactly you reached this conclusion is important, and explaining it clearly would help someone assist you with your research.
As you must already be aware, "James Thomas" is a rather common name, and more than one by this name had active-duty service.
All able-bodied free white males aged roughly 16-60 (varies by time and place) were obligated to serve in the County Militia for defense within the County. Most militiamen never saw active-duty service, but may appear on surviving muster rolls showing they turned out for regular drill (not considered active-duty service). Militiamen in that capacity might do such things as some patrolling, guard prisoners, or assist with escorting supplies bound elsewhere. Or, of course, be called out to respond to an alarm -- sometimes (but seldom) outside the County.
During the course of the war, militia units were sometimes folded into State Troops (standing armies created for defense within the Colony/State), and/or into the Continental Army. Each of the three organization types had their own functions, command structures and source of being paid: County, State, or Congress.
You appear to have found the listing for a James Thomas in Capt. Caleb Trowbridge's 5th Company, but you need also to mentally place the Company in its Regiment: the First CT Regiment (Continental) (1775). Giving this full description will also help others help you, as will the source of the listing: Johnston, Henry P., ed.. The Record of Connecticut Men in the Military and Naval Service During the War of the Revolution 1775-1783. Vol. I-III. Hartford, CT, USA: 1889, Vol. I, p. 41.
You have made good progress in your thinking to realize that you need some corroboration that your particular James Thomas was the one with this service.
One sort of clue is where his Regiment was recruited from. You can take a look at a brief history of the 1st CT Reg't. (Continental, 1775) here (click on American Troops link, then the State link):
http://www.myrevolutionarywar.com/index.htmIn order for it to *be* a clue, however, you need to have good documentation of where your man lived at the outset of the war.
At least one James Thomas (of Haddam, Middlesex Co.) was receiving a pension in the 1830s for his Revolutionary War service. He is listed in the above publication. If you have not looked at his pension application file, you'd need to do so, to determine whether he claimed service in Capt. Trowbridge's Company of the 1st CT Regiment (Continental). In fact, you would want to take a look at all pensioners under this name -- veterans with CT service moved to NY, to VT, to PA, to OH and elsewhere, so place of residence may very well not be the place served from.
Selected papers from pension files can be viewed at HeritageQuest, which your local library may subscribe to.
www.footnote.com has put well-indexed complete pension files on its site; while it is a fee site, short-term subcriptions and sometimes free trial periods are available. While you have the difficulty of a somewhat common name, the indexing at footnote.com is every-name, so it is possible that a living pensioner might mention your James Thomas.
Pensions were not available to non-officers who died in 1796 unless severely wounded while in service. I do not know what CT legislation there was on this point -- it may be something you want to investigate.
Not until the 1830s did Congressional legislation begin to allow pensions for widows of soldiers who served less than 3 years. If your man left a widow who lived into the late 1830s, it is possible that she applied for a pension under his service.
Another possibility is that, if your man was married before the war began, his wife may have applied to the Town they lived in or to the County Court for subsistence while her husband was away, particularly if they had young children. The CT State Library has a web site with a good summary description of what it has records for, and some information about where to find records that are not in its custody.
There are doubtless many CT sources that can help with developing evidence about your man's service. At the NSDAR web site are lists of local Chapters by location (under the membership tab), with contact information:
http://www.dar.orgEach chapter has someone designated to assist prospective members, so it is well worth while to contact a nearby chapter, explain what you know so far, and ask for assistance. The organization has quite a few very able researcher-coaches.
Good hunting!