Gunshots were heard in Braunstone and in the villages of Newbold Verdon and Glenfield earlier this month.
Property has been damaged in Braunstone, Newbold Verdon and Glenfield, detectives say.
Armed officers were called on Tuesday night and damage was found at a property.
Police say emergency services were called to Radford Drive shortly after 18:00 BST on Monday.
Six protesters have been charged with burglary and causing criminal damage.
Officers are negotiating with a group of people on the roof of a business premises, police say.
The council says the scheme includes roads close to Fullhurst Community College.
CQC inspectors have graded Jewel Home Care in Braunstone as "inadequate" overall.
