Single status is a noun phrase, so you need a noun as a Greek equivalent. I wish we had more context, as this can be a little tricky.

You would use the adjective ‘άγαμος’ for 'single' in a certificate, e.g.
Marital Status: Single
Οικογενειακή κατάσταση: Αγαμος

Ιn formal context, ‘single status’ would be ‘αγαμία’, e.g.
single status certificate = πιστοποιητικό αγαμίας

However, ‘αγαμία’ is formal and in everyday speech it refers to celibacy, life without sex.
So you would use roundabout ways of translating 'single status' in other cases, such as: το να είναι κανείς ανύπαντρος. Here are two examples lifted from the web:
- My single status has not gone unnoticed by some on the web. Το ότι είμαι ανύπαντρος δεν έχει περάσει απαρατήρητο…
- Single status is increasingly becoming a norm in society just as marriage is no longer a dominant force among the majority of the population. Το να μένει κανείς ανύπαντρος (i.e. Staying single)…

Incidentally, "ελεύθερος" (free) is often used to signify "single, unmarried".
There's this worn-out joke about taxi drives, where you ask them:
"Είσαι ελεύθερος;"
And their answer is:
"Παντρεμένος, δυστυχώς".


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Note added at 4 hrs 31 mins (2005-07-10 23:50:55 GMT)
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Correction: taxi driveRs