How do I get legal documents that signify my current marital status,
for use in getting married abroad?  The document needed is noted as
being an "apostyle."

This is for U.S. citizens residing in California (Los Angeles County),
getting married in The Republic of Belarus

Hi contundax,

You can either get an "Affidavit of Free Status" at the American
Consul in Belarus or a "Certificate of No Public Marriage Record"
through your county office in California. For the latter option, the
county clerk will issue the certificate, it will need to be translated
into Russian and then authenticated by the Secretary of State office
who will issue the Apostille. Give your county clerk a call and ask
about getting a "Certificate of No Public Marriage Record".

Marriage Requirements in Belarus
United States Embassy
46 Starovilenskaya St.
Minsk 220002, Belarus
Telephone: +375 17 210-12-83
"Certificate of Free Status (Certificate of Non-Impediment) - required
of all foreigners marrying in Belarus.  ZAGS offices generally accept
an "Affidavit of Free Status" executed before an American Consul in
Belarus (See on the Main Page - Consular Services: U.S. Citizen
Services; ... or before a notary public in the U.S. In the latter
case, the affidavit should be translated into Russian and
authenticated in accordance with the Hague Legalization Convention
(see http://travel.state.gov/hague_foreign_docs.html for additional
information on the Hague Legalization Convention and its procedures)
and bear an apostille. Documents issued in the U.S. can be
authenticated only in the U.S. The state where the document is issued
will need to affix the apostille."
http://minsk.usembassy.gov/html/marriage.html

Los Angeles County Clerk
Birth, Death and Marriage Records
(562) 462-2137 
http://www.lavote.net/GENERAL/Contact_Us.cfm

Notary Public
Authentication Information
Apostille or Certification
"The California Secretary of State provides authentication of public
official signatures on documents to be used outside the United States
of America. The country of destination determines whether the
authentication is an Apostille or Certification."
http://www.ss.ca.gov/business/notary/notary_authentication.htm

What is an "Apostille"?
"An ?apostille? is a certificate issued by a designated authority in a
country where the a treaty called the Hague Convention Abolishing the
Requirement for Legalization of Foreign Public Documents applies..."
What is a Public Document under the Convention?
"Article 1 of the Convention provides that for the purposes of the
Convention the following are public documents:
b. administrative documents such as civil registry records or office
of vital records regarding birth, death, marriage, etc.;"
http://travel.state.gov/law/info/judicial/judicial_2545.html

Sample Apostille:
http://hcch.e-vision.nl/upload/apostille.pdf

I was glad to work on this for you. If you have any questions, please
post a clarification request and wait for me to respond before
closing/rating my answer.

Thank you,
hummer

Google Search Terms Used: california apostille certificate no marriage
counties county

Thanks for your assistance.  I needed to be pointed in the right
direction, and this is exactly what your answer provided.