The incidents occurred in the areas of Burnside Road, Grampian Road and Granish Way in Aviemore between 10pm on Sunday, April 29 and 11am Monday, May 1.
Recognised for its skiing and hill-walking, Aviemore claims to have the lowest crime rates in the UK.
Police are appealing to anyone who has information or suspicions about these crimes, or who saw anybody in these areas between the relevant times to contact Aviemore Police Station on 01479 810222 or phone Crimestoppers anonymously on 0800 555 1111.