Question about the plot to Hostage (2005).

I was just trying to figure out this part of the plot. So in the movie, these robbers break into a man's house to steal his car, and things go wrong and it ends up turning into a hostage situation. The cops are called and Bruce Willis's character, a cop...

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His family is kidnapped by other criminals, who do not want the police finding a DVD in the man's house, that has incriminating evidence on it.

However, why would the police search the house after defusing a hostage situation?
If someone breaks into your house, and the alarm goes off alerting the police, and then the police come and defuse the situation, the police are then not allowed to say, oh by the way, we're going to search your home for anything incriminating to any crimes.

They are not allowed to do that, just cause they are responding to a break in and robbery, so why would the villains associated with the owner of house, have anything to worry about therefore?