Crime rate in MT is very low, almost nothing, THANK GOD! The cost of living depend on your lifestyle, what are you looking for? Average single family, 3 bedrooms/2bathrooms in Bozeman, around $220,000 (mortgage payment only $1,400) you can find good deals now because the buyer's market is really hot.
Please feel free to contact me for more information, I will be more than happy to help with all your questions about moving to Bozeman.
Have a great day!
Do you have a specific location in Montana in mind? If you need specific information about the Bozeman area visit the Prospera Business Group site. You will find a great economic profile on the area.