Under Nevada law, Republican county officials will appoint someone to serve the term in the Assembly to which Hof was elected.
Hof, 72, was found dead by porn actor Ron Jeremy on October 16 at the Love Ranch, one of the brothels Hof owned in Nevada.
"I know Republicans in Nevada got massacred tonight, but my man Dennis Hof crushed his opponent from the great beyond in AD-36 & we crushed the anti-brothel initiative in Lyon County by about 80%", Muth wrote on Twitter on Wednesday.
The Love Ranch brothel that Hof owned became notorious as the place where former Laker Lamar Odom was found unconscious in 2015.
Freakish though it may seem, Dennis Hof - who, as it happens, is also the owner of one of Nevada's most famous brothels - still won enough votes to be elected to the state legislature despite having been found dead on October 16. They're banned in counties that contain Las Vegas and Reno, and the state does not publicize how many are open. As a result, Nevada Republicans encouraged people to vote for him anyway.
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The pair then gave a united front in back-to-back press conferences, where they were both questioned over their relationship. These players are not good enough to play in a club as big as Manchester United and that has been going on for years.
Hof ran for office in 2016 as a Libertarian but lost the race. He said this was the best year ever.
The legal pimp had also been accused of sexual assault on at least four occasions.
Hof's campaign for District 36 - composed of Nye, Lincoln and Clark Counties - was marked by publicity stunts and billboard advertising that broadcast his pledges of repealing taxes and protecting gun rights, according to the US magazine The New Yorker.
He said Mr Hof "died quietly in his sleep" at Love Ranch - one of the brothels he operated in Crystal, Nevada.
The sprawling assembly district that touches both California and Utah and includes the Nevada National Security Site where nuclear weapons were once tested.