http://criminal.findlaw.com/criminal-rights/illegal-search-and-seizure-faqs.html
im not knox but this has a lot of info...
Doesn't change the fact that often people will let LE search the house especially if it will clear there name and help find the killer. Think the House to house search in the Jessica Ridgeway case. Let's say hypothetically that they could have found something in his house that could have lead the police to the person who kidnapped Katrina. Why would TS make the cops get a search warrant and waste a precious week.
For all we know someone that TS owed money could have kidnapped her as revenge.