Should any part of a county that has incurred a bonded indebtedness be cut off and annexed to another county, or erected into a new or separate county, the assessor of the county to which the segregated portion is attached, or the assessor of the new county created as aforesaid, shall, upon notice from the board of county commissioners of the original county from which such segregated portion was detached, given at the regular session of the board when county and state taxes are levied, collect in said segregated territory, and in addition to the other taxes collected by him for county and state purposes, and at the same time and in the same manner, the tax levied by said board of commissioners as herein provided; and the laws of the state relating to the levy and collection of taxes, and prescribing the powers, duties and liabilities of officers charged with the collection and disbursement of the revenue arising from taxes, are made applicable to this article. The money collected by the assessor as aforesaid shall be paid over by the treasurer of the county collecting it to the treasurer of the county losing the said territory, and for the purposes herein directed, but such segregated territory so attached to another county, or erected into a new county, shall be relieved of the annual tax, levied as provided in the foregoing section, when the county acquiring the same, or the new or separate county, pays to the county losing the territory, that proportion of the whole indebtedness, together with legal interest thereon, that the assessed value of property in the segregated territory bears to the assessed value of the property in the whole county, as constituted before the division or segregation thereof.