The standard OpenBSD Apache, no modifications at all, displays the following test page and css file well.
Code:
$ pwd
/var/www/htdocs
$ ls -l my*
-rw-r--r-- 1 www www 59 May 12 01:01 my.css
-rw-r--r-- 1 www www 617 May 12 01:22 mylinks.html
$ cat mylinks.html
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html;charset=ISO-8859-1" />
<link rel="stylesheet" type="text/css" href="./my.css" />
<title>My test page</title>
</head>
<body>
<div style="color: black; font-size: 80%; display: block ;">
<h1>Some links</h1>
<a class="ref" href="xml.html">XML, XSLT etc</a>
<a class="ref" href="openbsd.html">OpenBSD related stuff</a>
<a class="ref" href="freebsd.html">FreeBSD utilities </a>
</div>
</body>
</html>
$ cat my.css
.ref { display: block ; padding: 0.25em ; color: red ; }