Highlights (Related to American History)
NOTE on the Serial Set
Many important government reports and publications end up in the Serial Set, which is an annual volume(s) of materials submitted to Congress. If a Congressional speech or hearing references a document or report, it will usually be in the Serial Set. If you see a citation like "House Document 14" in a 1850 Congressional debate, go to the 1850 Serial Set volume & look at document 14. Special Reports also go into the Serial Set.
Later in the 19th century, especially after the Civil War, new federal agencies develop and begin publishing their own reports too.
The best way to find government publications is to search by agency. There is no good subject heading to help narrow just to government materials.
Search the agency as the author, and narrow further by adding keywords & narrowing the publication date.
You can also use "government printing office" as a keyword, which allows you to search across many agencies at once. The GPO is the printer for the whole federal government. This is not the best place to start because it is also listed as GPO, Gov. Pub. Office, and in the early 21st century it changed its name to Government Publishing Office.
Most state government publications, and nearly all federal government publications, are outside of copyright. This means most are freely available online via Hathitrust, Internet Archive, and GoogleBook. You can author search by agency in these websites to find their publications. Unfortunately it become hard to limit results.
I suggest identifying government publications in WorldCat, then searching the title of documents in Hathi & Googlebook; there is an extremely high likelihood the document is online. If it isn't check the main library catalog, which will search ProQuest Congressional & HeinOnline too.