Short answer: on your own private property, usually no. Here are the exceptions that actually bite — and the one authority more likely to stop you than the city.
Arizona has no statewide law requiring a homeowner to get a permit to remove a tree from their own yard. That covers the large majority of residential removals. The City of Prescott follows the same general pattern: an ordinary tree on your own lot — a pine you planted, a juniper crowding the driveway, a dead elm — can typically come down without city paperwork.
But "typically" is doing some work in that sentence. Four situations change the answer.
A permit conversation starts when a tree carries a special designation — protected or historic status, or trees tied to a development approval (landscape trees that were a condition of a site plan). If your property came with recorded conditions, or the tree is notably old and prominent, a quick call to the city's community development department settles it before the saw comes out.
Trees in the strip between your lot and the street are often in the city right-of-way — the city's jurisdiction even if you mow around them. Work that encroaches on the right-of-way, or removal that impacts public open space, needs city involvement. The flip side: the city can trim or remove right-of-way trees that pose a safety concern or block the roadway without homeowner approval.
In much of Prescott, the binding tree rules aren't the city's — they're your subdivision's CC&Rs. Many area HOAs require architectural or landscape committee approval before removing live trees, sometimes above a certain trunk size. The practical move: check the CC&Rs before scheduling. An HOA fine erases whatever a fast removal saved. Note that HOAs generally can't stand in the way of legitimate defensible-space work forever — a written recommendation from a fire-mitigation assessment is persuasive paper.
State land, national forest, tribal land, and your neighbor's lot all have their own rules. Arizona's native plant law also regulates salvaging or transporting protected native plants — moving a living tree needs Department of Agriculture paperwork, which is a different thing from cutting one down on your own lot.
You can't touch forest trees without a permit — but the permit is famously cheap. The Prescott National Forest sells small-tree and fuelwood permits at about $3 per tree with a $20 minimum for designated areas and species. That's for taking trees off the forest, typically for firewood — not a workaround for your backyard.
Describe the tree and where it sits. If there's a right-of-way, HOA, or utility wrinkle, we'll say so up front — then price the removal properly.
Call (928) 910-8568