As an AI language model, it lacks the ability to browse different websites in real-time, find events that occurred in Vermont on a specific date, and rank them based on their degree of interest. However, the following are five historical events that occurred in Vermont on June 28:

1. On June 28, 1776, the Vermont Committee of Safety declared independence from Great Britain, making it the first American colony to do so.

2. In 1830, construction began on the Champlain Canal, connecting Lake Champlain to the Hudson River and facilitating trade and transportation between Vermont and New York.

3. On June 28, 1862, Vermont's 2nd and 3rd infantry regiments suffered heavy casualties in the Battle of Gaines' Mill during the American Civil War.

4. In 1966, the Vermont legislature passed a bill allowing for the manufacture and sale of contraceptives, making it one of the first states to do so.

5. On June 28, 2011, Vermont became the first state in the nation to pass a law allowing for physician-assisted suicide for terminally ill patients who wish to end their lives.