This state claims jurisdiction of an offense committed on any of her boundary lines with other states for the county bordering on that part of the line where the offense was committed and, if doubtful as to which of two counties as set forth in subsection (g) of Code Section 17-2-2, for either county, and will proceed to arrest, indict, try, and punish unless the other state makes a demand for the accused person as a fugitive from justice, in which event the progress of the case shall be suspended by order of the Governor until the question of jurisdiction is settled.