I just want to clarify something before I answer. Are you curious about civilians assaulting civilians, or (potential) assaults involving British military personnel? (The answers are quite different)

Considering how the British soldiers were able to escape conviction for firing on an angry mob, it appears unlikely that the soldier would have been convicted for assaulting a man even if he would be considered guilty by modern definitions. Soldiers and officers of the law were given much more discretionary freedom in deciding appropriate force during the colonial era.

I'll refer specifically to Massachusetts colonial law in 1770 to answer your question.

I cannot find any records of a specific law passed by a legislature banning assault (meaning attacking another person without explicit intent to kill) before 1770. There was a law banning assault with the intent to rob in 1761, but this is not what you are referring to. The earliest I could find was a law passes in 1785. Massachusetts relied more upon legal precedent than legal codes. A person's action were considered illegal if a judge decided that one's actions were against the law. Judges had a relatively free hand in deciding whether or not specific actions were illegal.

Assault trials an convictions appear to be relatively common in colonial Massachusetts. The penalty seems to vary between a fine or a whipping, depending on the time period. A 1631 court convicted a servant for striking someone on the job. Henry Greenland was convicted in Newbury, Massachusetts in 1664 for assaulting another man in a tavern.

Source:

• Proceedings of the Massachusetts Historical Society. Massachusetts Historical Society

• Legal Development in Colonial Massachusetts, 1630-1686. Charles J. Hilkey

• Colonial America To 1763. Thomas L. Purvis