Answered for Carmel, Hamilton County.
Bark does not fall off living wood. Wherever it sloughs, the cambium underneath died some time ago and that section of trunk stopped moving water and sugar — the shedding is the aftermath, not the event. The number that decides everything is how much of the trunk's circumference is involved. A strip is a wound the tree grows around. A band all the way around is a girdle, and everything above it is finished whether it looks green today or not. In Carmel — Village of WestClay, Brookshire and Woodland Springs included, that's normally a tree trimming job at $250–$1,400. Not urgent.
Duke Energy Indiana. It runs a five-year distribution trim cycle, clearing roughly 20% of distribution line miles each year, gives Indiana customers a minimum of 14 days' notice before planned pruning, and files an annual vegetation management report with the IURC each March 31. Methods include pruning, mechanical trimming, brush mastication, herbicide application and hazard-tree removal.
Carmel Urban Forestry publishes an approved species list (last revised 3/28/2024) whose "Undesirable Trees" section reads like a field guide to what fills older Hamilton County streets: silver maple (shallow roots, weak wood), Callery pear, pin oak, red maple and all Fraxinus for emerald ash borer. Approved large street trees run to swamp white oak, bur oak, chinkapin oak, hackberry, male-only ginkgo, thornless honeylocust, Kentucky coffeetree, baldcypress and London planetree; note Callery pear is discouraged locally but is not yet banned in Indiana — 312 IAC 18-3-25 currently lists 44 species without it.
Carmel's code section 6-64 is titled "Planting and Removal of Trees and Shrub Regulations" and sits in the streets-and-sidewalks division of Chapter 6, alongside 6-55 covering trees and shrubs that obstruct streets and sidewalks — so the city's active regulation is aimed at the public way, plus landscape and buffer plantings approved through development plan review by Urban Forestry. I could not verify the exact text of 6-64 or confirm whether any permit applies to removing a tree standing entirely in a private back yard; contact Carmel Urban Forestry through the city's Department of Community Services before assuming, and check HOA covenants, which in most Carmel subdivisions are stricter than the city.
The strip between sidewalk and curb is city right-of-way, and Carmel Urban Forestry plants and maintains the street trees in it, including species selection. Many Carmel subdivisions layer a platted landscape easement and HOA covenants over that same ground, so two approvals can apply to one tree.
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Distance measured from Carmel.