Answered for Franklin, Johnson County.
The cambium — the living layer just under the bark that builds new wood and moves food down to the roots — was killed in that patch, and the tree is now conducting around a dead strip. A narrow strip gets grown over in a few seasons and leaves a scar. A strip that wraps far enough around leaves the tree partly girdled, and the crown above it thins as the remaining live tissue gets overloaded. Either way the exposed wood becomes an open invitation to borers and canker fungi that would not touch intact bark. In Franklin — Martin Place Historic District, Franklin Lakes and Knollwood Farms included, that's normally a tree trimming job at $250–$1,400. Not urgent.
Duke Energy Indiana serves Franklin, with Johnson County REMC on rural fringes. Because Duke is investor-owned it falls under the IURC's tree-trimming rule (170 IAC 4-9, from Cause 43663): at least two weeks' notice before planned trimming, and no removal of more than 25% of your tree and no topping without your permission, except in emergencies or where safe and reliable service cannot otherwise be achieved. JCREMC, as a co-op, is not IURC-jurisdictional.
Franklin is not among the 23 communities in the Indiana DNR street tree sample, so the two-tier picture here is inference from build dates rather than inventory: the pre-1935 blocks around Martin Place and the courthouse square carry the oldest, largest shade trees, while the late-1990s subdivision belt is now 25-30 years old and big enough that crowns are into rooflines and service drops. Ash is effectively gone to emerald ash borer, and the city Tree Board's approved street tree list governs what goes back into the right-of-way.
No permit is required to remove a tree in your own yard. Franklin's tree ordinance regulates STREET trees only: pruning, planting, treating, spraying or removing a street tree goes through a Tree Board permit, and topping is restricted. The ordinance's specific conditions — who may hold a removal permit, the trimming threshold, insurance and bond requirements and penalty terms — could not be verified from a retrievable source, so confirm them with the City before quoting right-of-way work.
The strip is the city's. Franklin's ordinance defines a street tree as one on real estate owned or controlled by the City, including anything in the public right-of-way, and an abutting owner may apply for a permit to plant or maintain a street tree at their own risk and expense. The ordinance is reported to treat trees within a set distance of the curb as city street trees where the right-of-way line cannot be determined — that presumption is unverified, so confirm the right-of-way line with the City before removing any tree near the curb.
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Distance measured from Franklin.