Answered for Carmel, Hamilton County.
Carmel went from 1,442 residents in 1960 to 18,272 by 1980, 37,733 by 2000 and 99,757 by 2020, so the bulk of the housing is 1970s through 2000s — I-465 construction beginning in 1967 set it off, and the town incorporated as a city in 1976. Old Town Carmel and Home Place, an early-20th-century interurban-era settlement annexed by Carmel in 2018, carry 60-to-100-year canopy, while the 1990s and 2000s subdivisions are on a first generation of nursery trees now 25 to 35 years old and just reaching conflict size. That's the thing that decides what a arborvitae here is likely to be — a mature specimen over a roofline, or nursery stock still establishing. Removing an arborvitae around Carmel runs roughly $100–$700, and in Village of WestClay, Brookshire and Woodland Springs access is usually what decides where in that range you land.
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 went from 1,442 residents in 1960 to 18,272 by 1980, 37,733 by 2000 and 99,757 by 2020, so the bulk of the housing is 1970s through 2000s — I-465 construction beginning in 1967 set it off, and the town incorporated as a city in 1976. Old Town Carmel and Home Place, an early-20th-century interurban-era settlement annexed by Carmel in 2018, carry 60-to-100-year canopy, while the 1990s and 2000s subdivisions are on a first generation of nursery trees now 25 to 35 years old and just reaching conflict size.
It is the default privacy hedge in every central Indiana subdivision, and the two things that end them are deer and ice. Because they go in as tight rows on a property line, one failed plant is a permanent visible hole that never fills — so arborvitae work is usually a replacement-and-reset job rather than a single removal.
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.
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Distance measured from Carmel.