If officers are conducting a search of the premises and they receive permission from one person residing at the residence, but a no from another one (this would apply to situation where there are roommates, married, etc...) the officers cannot conduct a search.
If they want to search they have to have a warrant.
What makes this case interesting is the background of it. Apparently it involved a feuding couple that was having a rocky marriage. The strain in the marriage was due to the husband's drug use causing money problems and she told officers that actual evidence of drug use is in the home. When the officers herd about the possible drug evidence they ask the wife if they can search the home, she said yes, while the husband said no. The officers entered the home anyway and discovered a straw with cocaine.
Chief Justice Roberts wrote a dissenting opinion that according to MSNBC was longer then the majority opinion. Justice Alito did not participate in the decision.

