Confused American

Have a look at this thread.

amerikanska.com/modules.php&file=viewtopic&t=22409&highlight=hinderspr%F6vning

It basically says you need to prove you are not married. Since there is no such document in the states sometimes you can get a paper stating that there is no such document.

Certificate of impediment before Marriage in Sweden

1- Physical attendance is required for those who are not Swedish residents.
This procedure is necessary in order to verify their identity. Swedish
residents do not need proof of identity. A national ID-Card from an EU
country is acceptable as means of identification. A passport is a necessity
for other citizens.

2-Non-Swedish residents that are citizens in a country where a visa is
needed (except Turkey and Egypt ) must show their visa and have an entry
stamp in their passport. Note that the visa must be valid in a Schengen
country but it does not matter if the validity has expired.

3- Non-Swedish residents must prove their civil status with a document that
is not more than four months old. It is possible for a certificate of
impediment to be issued without such a document, if there are difficulties
in obtaining a civil status document due to the fact that there is no civil
registration in their home country. However the dissolution of a former
marriage must always be confirmed by a document.

4- If neither of those intending to marry are Swedish residents or neither
of them has Swedish citizenship, it is necessary for an extract of the
marriage law of their home country or countries to be shown. This extract
may not be older than four months and should be issued by the competent
authority in their home country or countries.

5.In some circumstances a certificate of no impediment to marry containing
information on both partners may be shown instead of an extract of the
home country?s marriage law and civil status document.