A suit or action may be maintained by the State of Oregon or any county, incorporated city, school district or other public corporation of like character in this state, in its corporate name, upon a cause of suit or action accruing to it in its corporate character, and not otherwise, in the following cases:
(1) Upon a contract made with the public corporation.
(2) Upon a liability prescribed by law in favor of the public corporation.
(3) To recover a penalty or forfeiture given to the public corporation.
(4) To recover damages for injury to the corporate rights or property of the public corporation.