http://www.traduzione-localizzazione.com/consultazione/assev...

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Note added at 2 hrs (2013-06-08 10:43:52 GMT)
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I think this sentence is making the very simple point that the fact that a sworn document valid for one legal system is not necessarily valid in another legal system may impair the rights to a defence of one of the parties.

The context provided is not sufficient for me to motivate adequately this answer, which is based on a mere hunch.

I **suspect** that in this case "strumento" refers not to a document, but to a means (of proof), and that "asseverativo" has nothing to do (in this case) with the meaning of "giurare/to swear", but simply means "able to prove/to give evidence".





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Note added at 1 hr (2013-06-08 10:27:49 GMT)
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To put it simply, my take is that this excellent writer would have used the uselessly obscure expression "strumento asseverativo" to complicate readers' (and translator's) lives when he simply meant "strumenti di prova"...

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Note added at 1 hr (2013-06-08 10:28:22 GMT)
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...strumento di prova

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Note added at 1 hr (2013-06-08 10:38:19 GMT)
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or, better still, "mezzo di prova" (means of proof)

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Note added at 3 hrs (2013-06-08 11:46:46 GMT)
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My answer is based on the whole context of the source text, which is visible here:

http://www.proz.com/kudoz/italian_to_english/law_general/523...

"è noto che essi vantano diversi procedimenti di acquisizione della prova al giudizio ed una diversa “graduazione” dei poteri delle parti e di quelli del giudice (anche nella valutazione delle risultanze acquisite). Da tali diversità possono derivare rilevanti conseguenze sulla piena esplicazione del diritto alla prova, chiaro essendo che ogni "barriera" all'assunzione dei mezzi istruttori in altro Stato dell'Unione europea, ovvero alla variabilità della valenza di uno stesso STRUMENTO ASSEVERATIVO da una all’altra giurisdizione statuale, può risolversi in una limitazione del diritto della parte a “difendersi provando”.


Without knowing the enlarged context provided elsewhere, Thomas' answer is perfectly justifiable.

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Note added at 3 hrs (2013-06-08 11:47:59 GMT)
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And I was not honest when I referred to a "mere hunch" to motivate my answer.

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Note added at 8 hrs (2013-06-08 17:19:50 GMT)
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the key is here:

"all'assunzione dei MEZZI ISTRUTTORI in altro Stato dell'Unione europea, **OVVERO** alla variabilità della valenza di uno stesso STRUMENTO ASSEVERATIVO da una all’altra giurisdizione statuale".

**OVVERO** means that the writer is repeating the same concept by using different words. Ergo, "strumento asseverativo" = "mezzo istruttorio" = "mezzo di prova" = "means of proof". Simple! :-)

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Note added at 8 hrs (2013-06-08 17:23:39 GMT)
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http://www.grandidizionari.it/Dizionario_Italiano/parola/A/a...

asseverare
[as-se-ve-rà-re]
(assèvero)
v. tr.
lett. Affermare con risolutezza, asserire: a. un fatto, una notizia, un principio
‖ SIN. attestare


The author was simply meaning "means of proof", and had the very bad idea of using the almost never heard expression "strumento asseverativo".

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Note added at 8 hrs (2013-06-08 17:31:00 GMT)
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Asseverare = to assert, to affirm.

By using this awkward expression ("strumento assertivo"), he simply meant to refer to any means able to prove (assert) something, i.e. to any "means of proof".

As according to context, strumento is not a document; asseverativo= to assert, certify, so I suggest this, sworn/ certified before a notary