I use the following test documents,
test.tex:
\documentclass[a4paper,12pt,twoside,openright]{book}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{natbib}
\begin{document}
\tableofcontents
\chapter{Präfatßio}
Löräm ipßum dolor ßit amet, conßäctetur adipisiki älit, sed äüsmod tempor incidunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exärcitation ullamco laboris nisi ut aliquid ex ea commodi conßequat. Quis aüte iüre reprähenderit in voluptate velit eße cillüm dolore äu fugiat nulla pariatur. Exceptäür sint öbcäcat cupiditat nön proident, ßünt in kulpa kwi offitßia deserunt mollit anim id äßt laborum \cite{Wuersst1887}.
\nocite{*}
\bibliographystyle{apalike}
\bibliography{test}
\end{document}
and test.bib:
@BOOK{Wuersst1887,
title = {{The german umlauts - A pain in the ähß}},
publisher = {Springer, Berlin},
year = {1887},
author = {Hantß Würßt},
note = {Deutsche Ausgabe: Würßt, Die deutschen Umlaute ÄÖÜß, Springer, Berlin 1871},
owner = {asmaier},
}
On Mac OS X with basictex and latexml 0.8.2 I do the following
$ latexml test.tex > test.xml
$ iconv -f iso-8859-1 -t utf-8 test.xml > testutf8.xml # Necessary, because of problem #917
$ latexmlpost --dest=test.html testutf8.xml
When I open test.html in Chrome I see the following:

Note the encoding issues in the reference to the book and also in the author and title of the bibliography entry.
The bibliography file test.bib is stored as utf-8:
$ file test.bib
test.bib: BibTeX text file, UTF-8 Unicode text
The corresponding PDF output of latex and bibtex doesn't show these issues. So I guess, this could be an encoding issue in the bibtex processing of latexmlpost.
I use the following test documents,
test.tex:
and test.bib:
On Mac OS X with basictex and latexml 0.8.2 I do the following
When I open test.html in Chrome I see the following:

Note the encoding issues in the reference to the book and also in the author and title of the bibliography entry.
The bibliography file test.bib is stored as utf-8:
The corresponding PDF output of
latexandbibtexdoesn't show these issues. So I guess, this could be an encoding issue in the bibtex processing oflatexmlpost.