While Washington was still a territory in 1859, the US and Britain became embroiled in a conflict that became known as the Pig War. The events began because of the shooting of a pig, but the two were fighting over borders between the San Juan Islands, Vancouver Island, and the mainland. It ended ambiguously but ultimately the San Juan islands became a part of the U.S. and subsequently Washington. The "war" was actually a bloodless conflict and no shots were exchanged.
There are not a lot of primary sources in Special Collections related to the Pig War but there are a few historical accounts and papers for early pioneers who were in Washington at that time. There are also a wealth of secondary sources that can help you start your research. It can also be helpful to consult their bibliographies and see what primary sources they cite that we can help you find.