Any incorporated or unincorporated municipality or locality in the state having a population of less than 15,000, desiring additional physicians and wishing to be designated as a locality needing additional physicians, may apply to the Board of Medical Scholarship Awards to be placed on a list of localities in need of additional physicians, which shall be maintained by the board. Such applications may be made either by the municipal governing body or by a petition signed by at least one twentieth of the qualified electors of the municipality or locality. If the Board of Medical Scholarship Awards determines that such locality is in need of physicians, it shall place the locality on the list of localities in need of physicians from which recipients of scholarships may, upon graduation, select an area in which to practice. In compiling and maintaining the list, the board may place any locality thereon which, in its opinion, needs additional physicians.