(a) After the completion of any sewer or branch sewer authorized to be built under the provisions of this act, it shall be lawful for any municipality to which this act is applicable, whenever in its opinion the public health will be promoted by it, to order any one (1) or more property owners near or adjacent to any sewer to construct upon their property sewers leading from some point or place on their premises to the sewer of the municipality for the purpose of:
(1) Draining off surface or other water; and
(2) Conducting any excrement that may be at or about the premises and filth of every nature, character, and description into the sewers belonging to the municipality.
(b) In the order issued to construct the sewers for the purpose presented, the time within which they are to be completed, the nature and character of the material to be used in the construction of them, and the place of tapping the sewers of the municipality shall be designated, as well as the manner of doing it.