Any territory contiguous to a cemetery district and not within the boundaries of a city or town other than as set forth in RCW 68.52.210 or other cemetery district may be annexed to such cemetery district by petition of ten percent of the registered voters residing within the territory proposed to be annexed who voted in the last general municipal election. Such petition shall be filed with the cemetery commissioners of the cemetery district and if the cemetery commissioners shall concur in the petition they shall then file such petition with the county auditor who shall within thirty days from the date of filing such petition examine the signatures thereof and certify to the sufficiency or insufficiency thereof. After the county auditor shall have certified to the sufficiency of the petition, the proceedings thereafter by the county legislative authority, and the rights and powers and duties of the county legislative authority, petitioners and objectors and the election and canvass thereof shall be the same as in the original proceedings to form a cemetery district: PROVIDED, That the county legislative authority shall have authority and it shall be its duty to determine on an equitable basis, the amount of obligation which the territory to be annexed to the district shall assume, if any, to place the taxpayers of the existing district on a fair and equitable relationship with the taxpayers of the territory to be annexed by reason of the benefits of coming into a going district previously supported by the taxpayers of the existing district, and such obligation may be paid to the district in yearly installments to be fixed by the county legislative authority if within the limits as outlined in RCW 68.52.310 and included in the annual tax levies against the property in such annexed territory until fully paid. The amount of the obligation and the plan of payment thereof filed by the county legislative authority shall be set out in general terms in the notice of election for annexation: PROVIDED, That the special election shall be held only within the boundaries of the territory proposed to be annexed to the cemetery district. Upon the entry of the order of the county legislative authority incorporating such contiguous territory within such existing cemetery district, the territory shall become subject to the indebtedness, bonded or otherwise, of the existing district in like manner as the territory of the district. Should such petition be signed by sixty percent of the registered voters residing within the territory proposed to be annexed, and should the cemetery commissioners concur therein, an election in such territory and a hearing on such petition shall be dispensed with and the county legislative authority shall enter its order incorporating such territory within the existing cemetery district.