No appointment was necessary, I told the lady out front that I was willing to pay, and she took me in immediately... Things may have now changed.
I think... You would have to personally go there. I did have to prove that I was the daughter and neice of the deceased individuals. You also need to provide an approximate birth, marriage and/or death date of the person(s) you are searching. Also knowing the persons father's name helps.
Department of civil registration Horodenka District Department of Justice