There was no suspicion of a crime in progress or anyone in danger so they had no justifiable reason to enter. They weren't even there for her. It was to serve some dude a warrant.
From BPD own account -
"Yesterday, Gaines was being served with a “failure to appear” bench warrant stemming from charges incurred in a March 10, 2016 traffic stop in the area of Pikeswood Drive and Liberty Road. "
Edit, also relevant -
"New details of the incident are contained in an arrest warrant for Gaines, 23, who was shot to death by a tactical officer Monday after an hours-long standoff. Police obtained the warrant — charging Gaines with first- and second-degree assault and other charges — after they said they saw Gaines point a shotgun at an officer on Monday morning.
Officers initially went to the home to serve warrants on Gaines and her boyfriend, Kareem Kiean Courtney, 39, in separate cases. According to the newly released court documents, two officers arrived at the Carriage Hill Apartments on Sulky Court about 9:10 a.m. to serve Gaines and Courtney with those warrants." .
From -
http://www.baltimoresun.com/news/maryland/crime/bs-md-co-korryn-gaines-warrant-20160803-story.html .