You can use this helper function:
private string GetMimeType (string fileName)
{
string mimeType = "application/unknown";
string ext = System.IO.Path.GetExtension(fileName).ToLower();
Microsoft.Win32.RegistryKey regKey = Microsoft.Win32.Registry.ClassesRoot.OpenSubKey(ext);
if (regKey != null && regKey.GetValue("Content Type") != null)
mimeType = regKey.GetValue("Content Type").ToString();
return mimeType;
}