Although mule-ear over & under double rifles might seem unusual in some parts of the country, there were quite a number of New York State gunsmiths who made them. This one was made by Benjamin Losey, who was a member of a well known family of gunsmiths. Benjamin was the youngest son of Abiel Losey, and brother of John Losey, also gunsmiths. He was born in Otsego County, New York, June 12, 1816. He worked in Mott's Corners (now Brooktondale), New York, from the late 1840's through the mid-1870's, and in Syracuse, New York, 1879-1884. He died in Chicago, Illinois, March 13, 1896. There are many pages devoted to the Losey family and their various partnerships in Volume 3 of THE NEW YORK STATE FIREARMS TRADE by Holman J Swinney, compiled by Tom Rowe.
Judging from your pictures, I would say that this rifle has double-set triggers which will fire whichever barrel has the hammer cocked....or both of them, should the need arise.