You didn't say how long you have had your Zelkova. Is this your first autumn with it?
Zelkova are called semi-evergreen:
"Zelkova serrata/Japanese Elms are often sold as indoor bonsai and as such are acclimatised to indoor growing conditions, Japanese Elms sold as outdoor bonsai and all other species of Zelkova should be cultivated outdoors. Japanese Elms grown indoors (or in climates with very mild winters) will remain evergreen where as outdoor cultivation results in a deciduous tree. Ensure indoor trees do not become too cold in their first winter outside. Zelkovas should be able to cope with the adverse growing conditions indoors though they are never as vigorous as their outdoor counterparts.
(Indoors) Well lit, cool position on a sunny windowsill during the winter. Keep up humidity levels. Place outside from May onwards after last frosts have finished. Try to keep outside until Autumn when the leaves can be allowed to fall naturally before bringing indoors.
(outdoors) Outdoor Zelkovas/acclimatised Zelkovas are hardy to frost though temperatures below -5Â°C can result in fine branches dying back and root damage so should be afforded some protection. Frost protection can include placement in darkened outhouses and garages as when out of leaf Zelkovas do not require light. "
So if your tree has been indoors all the time, it might have stayed evergreen, but in nature it would be dropping its leaves and going dormant at this time.