This year, Independence day (4th of July) falls on a Saturday, should town offices be open or closed on Monday, July 6, 2020?

from Secretary of Commonwealth:

(1) Liquor Stores must be closed for Thanksgiving and Christmas Days. (1A) Liquor stores may not open prior to 12:00 noon Memorial Day. (2) Many companies operate all day on these holidays, pending obtaining a local permit. (3) All holidays falling on Sunday must be observed on Monday, under state law. Saturday holidays are observed on Saturday.

For a PDF version: Massachusetts Legal Holidays (PDF)

Above is a list of all legal holidays observed in Massachusetts. State, county, and municipal offices are closed on the days listed above. Federal offices are only closed on holidays which the federal government recognizes (i.e. New Year’s Day, Martin Luther King, Jr. Day, Washington’s Birthday, Memorial Day, Independence Day, Labor Day, Columbus Day, Veterans’ Day, Thanksgiving, and Christmas). The term “federal holiday” is not applicable to individual states and the private sector since each state has jurisdiction over its holidays.

In Massachusetts certain holidays are subject to laws which restrict the type of work that may be performed as well as the kind of business and commercial activities that may remain open. Only those holidays followed by asterisks (*) have certain restrictions. On holidays not followed by asterisks, business and commercial activities may operate as usual.