Sample connection strings configuration file from the Thinktecture IdentityServser setup for the associated blog.

connectionStrings.config

<connectionStrings>
  <!-- configuration data like endpoints, protocol config, relying parties etc... -->
  <add name="IdentityServerConfiguration"
       connectionString="server=.;initial catalog=IdentityServerConfiguration;Integrated Security=SSPI" 
       providerName="System.Data.SqlClient" />
  <!-- user database -->
  <add name="ProviderDB"
       connectionString="server=.;initial catalog=AuthDemoApp;Integrated Security=SSPI" 
       providerName="System.Data.SqlClient" />
</connectionStrings>