I think it depends on whether there were exigent circumstances. If her body had already been removed and the cleaning had already occurred, they'd probably need a warrant. If the crime scene was being cleaned, probably not, since they'd need to stop the cleaning to preserve evidence.

The whole thing stinks of a cover up though, from the police telling landlord to clean it to the examiner finding suicide. It makes you wonder whether there were envelopes full of money, or whether the examiner was covering up for the cop who recommended cleaning.