The couple - who have children North, six, Saint, three, Chicago, 20 months, and Psalm, four months, together - recently splashed out $14 million on a ranch in Cody but local residents of the small town are said to be ''apprehensive'' about the attention they will bring to the area.
The Public Information Officer for the Cody Police Department told RadarOnline.com: ''Residents are set in their ways. It'll be a learning curve for them to get used to the way people are around here.
''It is a quiet place. There are some who are upset about the move. Some are apprehensive. Because of their notoriety and headlines, people are scratching their heads.
''People don't like when you move from out of state and try to change the way the people are around here. The residents are down to earth and private.''
However, the officer stressed ''most'' residents don't mind having the famous pair joining their community.
He said: ''Most people feel like me though. They're far enough out of town and they have no neighbours. I hope they enjoy their ranch.''
The 'Keeping Up With the Kardashians' star recently admitted she thinks Wyoming is an ''amazing place'' but she and her family will only be spending weekends and holidays there, rather than relocating from Los Angeles for good.
She said: ''We love Wyoming. It's always been an amazing place. My husband did just buy a ranch there. His dream and his vision is to move there. I love LA, so I envision summer, I envision some weekends, but yeah, we love it. It's the prettiest place you've ever seen in your entire life.''
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