NH Law About ...: Shoveling Sidewalks: Read the Law About ...

RSA 230. State Highways
See RSA 230:81 Snow, Ice and Other Weather Hazards
RSA 231. Cities, Towns and Village District Highways
See RSA 231:92-a Snow, Ice and Other Weather Hazards
RSA 236. Highway Regulation, Protection and Control Regulations
RSA 236:20 is about snow obstruction on roads.
RSA 507-B. Bodily Injury Actions Against Governmental Units
See RSA 507-B:2-b Snow, Ice, and Other Weather Hazards.
RSA 508. Limitation of Actions
See RSA 508:22 Liability Limited for Winter Maintenance

State v. Jackman, 69 N.H. 318 (1898)
State v. Jackman, 69 N.H. 318 (1898) is the case so many newspaper articles refer to when they write about snow removal. It's difficult to find case law this old online, so we've scanned the print version and uploaded it.

Rutkauskas v. Hodgins, 120 N.H. 788 (1980)
The principal issue in this case is whether the owner of a building which redirects precipitation, thereby causing an accumulation of snow and ice on a public sidewalk immediately adjacent to the building, is strictly liable to a tenant who is injured by falling on the snow-covered sidewalk. We hold that there is no such liability.
Ritzman v. Kashulines, 126 N.H. 286 (1985)
On January 17, 1982, Jane L. Ritzman slipped and fell on a natural accumulation of snow on the shoulder of Main Street in Hopkinton. Mrs. Ritzman fell while walking toward the sidewalk in front of the defendants' store, The Cracker Barrel. The area where she fell is used for parking by customers of the store and has been periodically plowed by the defendants.

2007-0618. Tinker v. Town of Tilton
The plaintiff brought an action seeking injunctive relief that would require the Town to make the section of sidewalk at issue accessible to persons with disabilities by removing snow from it during the winter months.
2009-0012. Tinker v. Commissioner Dept. Of Transportation
[T]o the extent a sidewalk is deemed part of a “facility” that is “required to be readily accessible to and usable by persons with disabilities” under the ADA, the maintenance obligations of the public entity having control over the sidewalk include the reasonable removal of snow, ice or debris rendering the sidewalk inaccessible. Because, as noted above, the town concedes that 28 C.F.R. § 35.133 applies to the sidewalk at issue, the trial court did not err by concluding that the town’s maintenance obligations relative to it include the removal of snow, ice and debris. ... The refusal to remove any snow is not a reasonable limit upon the removal of snow, but is an abdication by the town of its obligation altogether.

These are examples of some local town and city ordinances dealing with snow removal.

Shoveling Sidewalks