There is no specific search software for the downloads section indeed. But as every uploaded mod automatically generates a forum thread you can use the default forum search.
Personally I never use the default forum search as the results aren't good enough for me. I always use google to search the RD site with "site:racedepartment.com" as an addition in the search query. Still gives me the closest results.
Ill have a look if we can get a search function directly for the downloads though, thanks for the suggestion.