A quick read of this NHDES publication says new docks can't be placed within 20 feet of the imaginary property line that extends over the water, unless notarized permission is given from the adjacent property owner. More interesting is Figure 2 and associated text, which states the boat space (6' from dock) can never cross the imaginary property line in the water.
https://www.des.nh.gov/sites/g/files...0-01/wb-19.pdf
Now, the OP is dealing with an existing dock, and not a new one, so grandfathering may occur. Plus there's the whole political issue of dealing with a neighbor; you might be able to make a legal case for a change but you still have to live next to that person, no matter how upset they are at you.