A good place to look up German tool stamps is this site (by Wolfgang Jordan):
http://www.holzwerken.de/museum/hersteller/marken.phtml
Listed for "Turm" are these four makers:
Turm = Rhein. Werkzeugfabrik Rich. Peiseler Remscheid
Turm, unten viereckig, oben rund, mit spitzem Dach = Süddeutsches Präzisionswerk A.-G., Geislingen-Steige
Turm mit Fahne = Rhein. Werkzeugfabrik Rich. Peiseler, Remscheid
Turm mit zwei Fahnen = Ed. & Ad. Boehm, Remscheid
The one that might be a match is:
Süddeutsches Präzisionswerk A.-G., Geislingen-Steige
with the stamp described as:
"Tower, square below, round top, with a pointed roof"
(translated by google)
In the stamp on the axe, there is a tower with a square at the bottom, the top portion of the stamp is round, and the "roof" of the tower does look like it could be pointed (like a gable).