WWI Medic hand axe ?

Hello, I'm new to this site and would like some help with this item I picked from an 1920's Wisconsin Mansion that was having an estate sale. Many of the Military Medic items were over my price range but I managed to find this US issued hand axe that was in another room with the right price. I had no idea at the time that medics were issued the m-1910 hand axe for making stretcher poles in the field and I was just going to use it for yard work around the house till I did a little bit of research. The axe handle I found was brushed thick in olive drab and I could see some lightly engraved letters under the paint. After removing most of the paint I found that it reads, " LT. W. M. MARTIN 32 A 120 FA" It must have been ingraved in black on the natural wooden handle then painted OD some time later. This area of Wisconsin is near where the 1917-1918 WWI 32nd Division Battery A 120th Field Artillery originated from. This officer's name is not listed on the WWI 32nd Division Wisconsin book. Is there a way to find out if this belonged to a Medical Corps officer? I don't think a Field Artilley LT. would be carrying a hand axe in the battle field. I read that the M-1910 hand axe was part of the standard Medical Corpsman issued gear.