There does not seem to be a documented close lineal connection between August Dvorak and composer Antonín Dvořák, although it would be reasonable to suppose some relation exists.
"I'm told there is a relationship, but I can't prove it."
John knows who his uncles are. His father is Walter Charles Dvorak born in Minneapolis to John Steve Dvorak (also born in Minneapolis). August Dvorak and all of his siblings (none of them Walter) were all born in McLeod County to IMMIGRANT Joseph Dvorak. If there's a connection it goes back to Bohemia.