I passed through there 2 days ago. I wasnt asked for insurance docs but they were very thorough in cross checking my vehicle owner's document with my passport details. Whole process took about half an hour, they were very friendly and there is a woman ther who speaks English. Only bad thing was I only got a 3 day transit visa.
They warned me that the Ukraine - Romania border was not gteat so I exited through Hungary in the end.
One bit of advice - do not queue at these borders- bikes are expected (and encouraged to push to the front!
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