In a town having a municipality within its limits, authorized by law to construct main sewers, drains, and outlets at the expense of the abutters or those interested, where a sewer, drain, or outlet will benefit those outside the limits of such municipality as well as those inside, upon petition of a majority of those interested in its construction, setting forth that they are liable to contribute towards its expense and that the public health and convenience demand it, the selectboard may join the proper officers of such municipality in laying out and constructing the same.