I asked the guy who used to be the Environmental Officer at the Apokoronas Dimos offices in Vrysses. Here is his answer:
Cypress trees fall under the jurisdiction of the forest law, so you need to have obtained a felling permit from the forestry department in Hania. That is if the tree or trees lie outside of the official village boundaries (as determined by law). In the case that the tree lies within the village boundaries then the owner need to have obtained at least a permit from the municipality (the environment office in Kalyves). I think there could be an obligation to obtain a permit from the building authority in Hania (where you get building permissions), I am not sure about the latter. I am not sure also which criteria (if any) the municipality considers for tree felling or not. FYI the council reached to the forestry department and they collaborate for the felling of damaged, sick or already felled trees so that the firewood could be supplied to families in need. So if you know areas where trees are damaged or became a public hazard during the last storm you could reach out to the municipal social enterprise (Mrs Benaki).
Apokoronas Environment Group
Yesterday today was tomorrow. Don't dilly dally!