You don't need to have a criminal record for the police to search your home. Breonna Taylor's ex-boyfriend was a known drug dealer who was seen picking up packages from her apartment and driving to a drug house, Taylor was also seen in surveillance with her ex-boyfriend driving to drug houses in her car. The police had probable cause to search her home because her ex-boyfriend listed her apartment as his address a month before the raid. There's plenty of reasons for the police to suspect that either Breonna Taylor or her apartment was involved with her ex-boyfriend's drug trafficking based on surveillance, recorded jail conversations of her and her ex-boyfriend discussing drug houses, her posting bail in amounts of $5000 to her ex and his drug dealer associate, and the fact that a dead body was found in her car after she let her drug dealer boyfriend borrow it.

The fact is that Breonna Taylor has been on the police radar in their drug trafficking investigation for months because of suspicious activity which finally led to police to get a warrant signed off by a judge to search her apartment which led to her shooting death after Kenneth Walker fired a gun at the police. The police also found evidence that Walker was also involved with illegal drug dealing and a possible robbery from texts from his cell phone when they investigated him for attempted murder and it's possible he might be facing charges after the FBI is done with their investigation.

He's also initially claimed that Breonna Taylor was the one who shot at the police:

https://www.wdrb.com/news/body-camera-video-shows-frantic-moments-after-fatal-raid-on-breonna-taylors-home/article_1ec98154-080c-11eb-a45c-abdc67f16c12.html

HANKISON: "Where is she at in the apartment?"
WALKER: "She's on the ground."
HANKISON: "Where at?"
WALKER: "In the hallway."
UNKNOWN OFFICER: "What kind of gun did SHE shoot?"
WALKER: "It was a regular 9mm."
HANKISON: "Did she shoot or you shoot?"
WALKER: "It was her. She was scared."