In general, the Austrian Nationality Act does not allow dual citizenship except for persons who obtain two citizenships at the time they were born (e.g. a person born to Austrians living in the US acquires both Austrian and US citizenships at the time of birth).

Thus, if a person acquires US citizenship, he/she usually has to renounce the actual citizenship he/she is holding. The only exception is stated in Section 28 of the Austrian Nationality Act:

A person shall be permitted to maintain Austrian citizenship
a) if the maintenance is in the interest of the Republic of Austria, or
b) if personal reasons are worth considering (the law does not provide for examples of specific reasons that are worth considering but one may think of older relatives living in Austria, career prospects, reasons related to property issues etc.).
Only born Austrians may make use of this legal provision stated under b).

The authorities in Austria charged with deciding on the granting of dual citizenship are the "Ämter der Landesregierungen" (provincial governments) of the province where the applicant had his last residence in Austria. If the Austrian was born abroad and never lived in Austria, the "provincial government of Vienna" will handle the case.

The application to keep one's Austrian citizenship, a written request addressed to the "Amt der Landesregierung", together with
a) certified copies of the birth certificate
b) the certificate of citizenship,
c) the marriage certificate (if applicable),
d) a detailed curriculum vitae, and
e) criminal records (certificates of good conduct) from all countries where one lived for more than six months (please be aware that the issuing police department(s) could ask you for a letter from the Consulate in which it is stated that the certificate is required by the Consulate)
will be forwarded to the provincial government handling the case.

Please note: An Austrian citizen who wants to keep his/her Austrian citizenship in the case of acquiring US citizenship MUST be granted the right to keep the citizenship before he/she pursues any steps directed at obtaining US citizenship. The right to keep one's citizenship is granted (if it is granted) under the condition that US nationality is then acquired within a period of two years. As soon as it becomes known that US citizenship will (most likely) not be obtained within these two years, please file for an extension immediately.

Extracted from; http://www.aussenministerium.at