In standard mandarin: 茶館
In standard mandarin: 察館
IPA for both: t͡ɕa̠kã̠ɴ
In standard mandarin there is no difference as they are homophones, pronounced exactly the same. However, please keep in mind that mandarin is spoken in multiple countries and across billions of people. Most people do not speak completely standard mandarin-- unless they are a newscaster getting fined or dubbing a drama.
It's very likely the difference that you are talking about is specific to the locality, or perhaps an accent to mandarin from another chinese language. I recognize 察館 as a visual pun to refer to being called in by the police to "drink tea", but do not know which area may pronounce it differently. If you have any info on the relevant area, it will be possible for us to try to find the pronunciation difference for you.