I would include "non-marriage" for two reasons. First, because "negative certificate" alone is not a term commonly used in English (except apparently in the Philippines), and second, because there are different kinds of "certificado negativo", and unless the context makes it clear beyond any possible ambiguity that it is this kind, it could cause misunderstanding. For example, there is a negative criminal record certificate, which could be relevant here; it's apparently required for a foreigner to be able to marry in Brazil, for example ( https://www.proz.com/kudoz/english-to-portuguese/law-general... )

I don't think it's overtranslation; in English it is normal to specify the type of "certificado negativo", whereas in Spanish it is normal not to.

--------------------------------------------------
Note added at 1 day 32 mins (2018-11-14 14:10:36 GMT)
--------------------------------------------------

Daniela: If you prefer "single status certificate", fine. It makes no difference at all: single status is non-marriage and non-marriage is single status.

From the description you've now provided, this is simply a certificate of marital status. Why then do they refer to it as a "certificado negativo"? It can only be because it is negative with respect to being married: it certifies that the answer to the question "is this person married?" is in the negative. "Non-marriage" has at least the virtue of reflecting "negativo". But after what you've said I feel more strongly than before that the literal translation "negative certificate" would be unsatisfactory. I simply don't think it will be understood; I wouldn't understand it. I repeat, the only thing that is "negativo" about the certicate as you describe it (datos personales y estado civil: soltero) is that it is negative with respect to marriage.

--------------------------------------------------
Note added at 1 day 34 mins (2018-11-14 14:12:56 GMT)
--------------------------------------------------

I mean, it would accurate to call it a "certificate of marital status", since that is what it apparently is, in fact. But that is not really a translation of "certificado negativo".

--------------------------------------------------
Note added at 1 day 37 mins (2018-11-14 14:15:22 GMT)
--------------------------------------------------

You can't call it a "negative certificate of marital status", because that would mean that the person has no marital status (i.e., no "estado civil"), which is not true: soltería is a marital status.

--------------------------------------------------
Note added at 1 day 7 hrs (2018-11-14 21:36:22 GMT)
--------------------------------------------------

"Certificado negativo", según parece, es una expresión normal en el lenguaje de los funcionarios del registro civil (supongo que se trata de Argentina):

"Códigos, trámites y valores
[...]
(226) Por cada certificado negativo $ 32,50.
(594) Por cada certificado de estado civil $106,25."
https://losandes.com.ar/article/desde-dni-a-divorcios-hacer-...

Si consultamos la Ley Impositiva (esta es la de la provincia de Córdoba, pero en otras se emplean los mismos términos, encontramos lo siquiente en el apartado de Registro Civil:

"“Por cada copia o fotocopia de acta, certificado, extracto, certificado negativo de inscripción, constancia de estado civil o supervivencia”
http://web2.cba.gov.ar/web/leyes.nsf/0/fe5af60f5aca8ebe03257...$FILE/10250%20IMPOSITIVA%202015.pdf (Art. 82)

Es decir, que "certificado negativo" debe de significar "certificado negativo de inscripción", o sea, "certificate of non-registration". La inscripción puede ser de nacimiento, matrimonio o muerte.

Me parece que hay una anomalía aquí, porque tal como lo describes, parece que se trata de un certificado (o una constancia) de estado civil.

En cualquier caso, me parece legítimo y necesario traducirlo haciendo explícito lo que está implícito en el texto fuente: es decir, que "certificado negativo" significa en realidad "certificado negativo de inscripción", y que la inscripción en cuestión es de matrimonio.