Hi leeplatt
If you want to Configuring membership provider by connectionString, please open the web.config file of publish website and add the following markup
<membership defaultProvider="mymembershipprovider">
<providers>
<clear/>
<add name="mymembershipprovider"
type="System.Web.Security.SqlMembershipProvider, System.Web,
Version=2.0.0.0, Culture=neutral,
PublicKeyToken=b03f5f7f11d50a3a"
connectionStringName="LocalSqlServer"/>
</providers>
</membership>
<connectionStrings>
<add name="LocalSqlServer" connectionString="Data Source=sql2005;Initial Catalog=northwind;Integrated Security=True" providerName="System.Data.SqlClient" />
</connectionStrings>
Hope it helps