now Tirol is a state of Austria not a district. ;-)
for the east-tyrolean Asch belonging to Anras you can ask at tyrolean country-archive in Innsbruck. they have the churchbooks mircofilmed. so you can clear up if this ancestor is to find in this small alpine place in the mountains. think this info must be free: http://www.tirol.gv.at/themen/kultur/landesarchiv/
churchbooks would exist for Anras since 1633.
but think also more for Bohemia, now Czech Republic.
it´s very close to german states Bavaria and Sachsen: https://maps.google.at/maps?hl=de&q=A%C5%A1+Czech+Republ...
"Czechoslovakia" does not longer exist.
The Czech Republic and Slovakia was established on 1 January 1993 by the division of Czechoslovakia.