As one of the results of WW 1 that created Slovenia as part of the new Kingdom of SHS, the comitate (county) of Vas lost its southernmost district of Muraszombat. This was the district which included Borháza.
As Mohnbauer already mentioned, about two thirds of the 300 or so inhabitants of Borháza were Roman-catholics, and one third were Lutherans.
The parishes for both religions (and therefore the official recording of vital events till September 1895) were in Felsöpetrocz, formerly Péterhegy. LDS has microfilmed the duplicates of the records of both religions starting in about 1828.
Felsöpetrocz was also a location for civil recording which took over starting on Oct. 1, 1895. I think it is likely that Borháza belonged to this civil recording district. Another candidate town would be Felsölendva.
The entry for the church records of Felsöpetrocz in the LDS library index has an apparent error, because in the second and third line, the two religions are exchanged. Anyway, "carichak" has a good chance to find data on his ancestors via the LDS microfilms.