In what circumstances will police obtain consent to search the home of an alleged co-defendant?

In Matlock a bank robber was arrested in front of his house. Without asking the defendant which room he occupied or whether he would consent to a search of the same, some of the officers went to the door of the house and were admitted by a woman. Without ascertaining her status other than that she jointly occupied a room in the house with the defendant, the officers obtained her consent to look for the money taken from the bank and the gun used in the robbery. Apparently, she gave permission to search the entire house. The incriminating evidence, which was the subject of the motion to suppress, was found in the bedroom which she alleged occupied jointly with the defendant. The majority opinion, concurred in by the six Justices, found little difficulty in concluding that:

United States v. Matlock, supra, 415 U.S. at 171, 94 S.Ct. at 993.