The owner of personal property, removing from one county, town, or district to another between January 2 and March 1, shall be assessed in either in which the owner is first called upon by the assessor. A person moving into this state from another state between those dates shall list the property the person owns on January 2 of such year in the county, town, or district in which the person resides, unless it appears to the assessor that the person is held for tax of the current year on the property in another state.