Answered for Carmel, Hamilton County.
Climbing ivy is not a parasite. It does not tap into the tree or feed on it, and light growth on a lower trunk is close to harmless. Three real problems arrive later: the vine adds substantial weight and a great deal of wind-catching surface high in a crown that never evolved to carry it; it shades out the tree's own foliage once it spreads through the canopy; and — the one arborists care about most — it hides the trunk, so nobody can see a crack, a cavity, a conk, or an old wound underneath. A tree in a full ivy jacket cannot be properly inspected. In Carmel — Village of WestClay, Brookshire and Woodland Springs included, that's normally a tree trimming job at $250–$1,400. Not urgent.
June 29, 2023 derecho — Carmel logged several medium-sized limbs down while the same line measured 70 mph at Indianapolis International. The July 15-16, 2024 derecho tracked directly through Hamilton County with damage at Westfield (about 55 mph), Cicero and Atlanta, including a barn hit by a gustnado near Atlanta. September 14, 2008 remnants of Hurricane Ike brought 50-70 mph gusts for hours across central Indiana.
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.