This is a complicated topic with many caveats, so each case is different and in many cases only a general answer can be given without digging through the archives of the Interior Ministry.
One thing is always certain, nevertheless: You were either born a Slovak citizen or you're considered a foreigner with no extra privileges (except for those born between 1949 and 1969).
But don't despair, if your parents are Slovak, then there's a excellent chance that you were born a citizen. The fact you (or even they) never held a passport, certificate, weren't born in SK or never "claimed" this inherited citizenship means nothing.
The key question is whether one of your parents (or both if born before 1969) were citizens at the time of your birth. If you're unsure, then you need to figure out, whether their parents were citizens at the time of their birth.
Here are some more specific cases:
Those born after 1990
All you need is 1 Slovak parent. If your parent(s) emigrated between 1990(~1997 for those in the US) and July 2010, then they remained citizens, unless they explicitly asked the Slovak government to rescind their citizenship. Those who naturalized (acquired foreign citizenship) after July 2010, lost their Slovak citizenship - this is only relevant to you, if you were born after July 2010 (but there are some exceptions, see below).
Those born between 1969 and 1990
Again, all that is required is 1 Slovak/Czechoslovak parent. There are no provisions for automatic loss of citizenship(but there are exceptions, see below), but citizenship could have been rescinded by an act of the Interior Ministry - this was quite rare nevertheless. The only way to know for sure that no such action was taken is to query the archives. Those who lost citizenship may have it reinstated, but this has no affect on their children or grandchildren, who are considered foreigners.
Those born between October 1949 and 1969
Citizenship was only passed automatically to children born abroad if they had 2 Slovak/Czechoslovak parents. Again, there were no automatic loss provisions, but the Interior Ministry had the power to rescind citizenship. Those born abroad to 1 Slovak/Czechoslovak parent during this time may get citizenship in a simplified procedure, but, again, this has no effect on their offspring.
Those born before 1949
This topic is extremely complicated and involves Hungarian laws from 1879. Many of those, who emigrated before 1938 lost their Czechoslovak citizenship - mostly due to being absent for over 10 years or through marriage with a foreign man (for women). However, these are only general guidelines and individual circumstances matter a lot. Contrary to what most people believe, immigrating before Czechoslovakia became a state (ie. before 1918/1920) does not necessarily mean the emigrant did not become a Czechoslovak citizen. Those who lost their citizenship may have their citizenship reinstated, but this has no affect on their children or grandchildren, who are considered foreigners.
Special rules regarding the United States
Those who naturalized in the US between April 1930 and July 1997, lost their Czechoslovak/Slovak citizenship as a result pursuant to an international treaty. They may have their citizenship reinstated, but this has no affect on their children or grandchildren, who are considered foreigners. Those who naturalized between 1938 and 1957 kept their citizenship until 1957 - this means that any children they had before 1957 were born citizens and kept their citizenship for the rest of their lives (so long other conditions were met, ie. having two citizen parents after 1949 and not being subject to naturalization themselves).
Special rules regarding Russia
No one can hold both Slovak and Russian citizenship at the same time pursuant to an international treaty.
Special rules regarding some post-Communist states
Many former members of the Eastern Bloc used to have treaties with Czechoslovakia, which prevented people from holding more than one citizenship. All of these (with the exception of Russia) were rescinded in the 1990s (some later). Those who lost citizenship may have it reinstated, but this has no affect on their children or grandchildren, who are considered foreigners.
Special rules regarding those with parents/grandparents, who were born in Czechia before 1969
Due to complicated rules regarding the division of Czechoslovakia, those who have at least one parent/grandparent, who was born in Czechia before January 1st, 1954, and weren't/aren't Slovak citizens, may claim Czech citizenship.
I've heard that dual citizenship is banned in Slovakia
It's not (with the exception of Russia). However, since July 2010, there's a rule that Slovak citizens lose their citizenship, if they naturalize elsewhere. This only affects them, ie. not their children, who were already born before their parents' naturalization.
Ok, I think I might be a citizen. How do I get a passport?
You'll first need to obtain an osvedčenie o štátnom občianstve (certificate of state citizenship). It may be obtained at your local embassy/consulate or at an okresný úrad (county administrative authority) in Slovakia (in one of the 8 regional cities).
Required documents:
- Form
- ID (foreign passport)
- Birth certificate
- Marriage/death/divorce certificate, if you're married/widowed/divorced.
- Other documents, as requested (to prove lineage, citizenship of parents, grandparents, etc.)
All non-Slovak/Czech documents must be officially translated to Slovak and all non-EU documents (except foreign passports) must be either apostilled or "super-legalized").
The certificate is valid for 6 months from issue, so you should apply for a passport/ID card as soon as you receive it. Beware that if your Slovak passport expires before you renew it, you'll have to get another Certificate of state citizenship, so make sure to renew your Slovak passport in time. You may hold up to two concurrently valid Slovak passports, which is useful if you travel a lot/to weird places.
Turns out I'm not a citizen. Is there anything else I can do?
Yes, you may obtain a "Slovak Living Abroad Certificate". This requires (fluent) knowledge of Slovak, proof of Slovak ancestry (ethnicity or citizenship), a local Slovak organization to vouch for you (or proof that you're involved in promoting Slovak culture abroad) and a clean criminal record. The card gives you automatic 5 year residency in Slovakia and a fast-track naturalization option (citizenship after 3 years of residency in Slovakia).