Are you sure you want a redirect? Using a 301 redirect will 'inform' the client (such as a browser or search engine) that the URL has been permanently changed and that it should discard the old URL and use the new one instead. In this case, that means that your previous work to create and use 'search engine-friendly' URLs will be destroyed, and visitors and search engines will see and use the ugly script-filepath-plus-query-string URLs from now on.
99.99% of all posters here want to go the other way -- from ugly query-string-based URLs to static-looking "search-friendly" URLs.
To your direct question, though: Do you have other working rules in this file? If not, then you may be missing the required 'setup' directives needed to enable mod_rewrite. Or maybe you've got interference from mod_negotiation, mod_spelling, or AcceptPathInfo.
You will need some variant of both of these directives at the top of your mod_rewrite code, or only the second one. The only way to find out is to test:
Options +FollowSymLinks -Indexes -MultiViews
RewriteEngine on
On Apache 2.x, you may also need:
AcceptPathInfo off
The Options settings I show in addition to +FollowSymLinks are typical, but you should look them up in the Apache "core" documentation and make sure each is appropriate for your server and site.
Minor problem, but likely non-fatal in this case: You should specify the protocol and hostname for external redirects, and you should not link to "index.php" -- just link to "/" plus the query, and let mod_dir handle the index script filename:
Rewriterule ^([^-/]+(-[^-/]+)*)-county/([^-/]+(-[^-/]+)*)-md/homes-for-rent-page([0-9]+)\.html$ http://www.example.com/?action=searchresults&PageID=searchresultssef&County=$1&city=$3&ForSale=N&cur_page=$5 [R=301,L]
Jim
