ASP.NET SQL Server Connection with domain security

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ASP.NET

SQL-Server

Hello Guys,
Anyone know the best way to initiate SQL Connection to MS SQL Server with a domain security? (Domain security is very important here and makes the most problem).
In other words - I need the server somehow to identify you as a user (without asking for passwords and stuff) and based on that - deny or grant you to use the resources (hide/show datagrid).
I have server configured and AD group created for that purpose.

From WPF interface I am using "Trusted_Connection=True" in a connection string, but the same thing in ASP.NET somewhy does not quiet work. So in other words - it works perfectly on non-web application.

Small guidance or a pointer here or there would be really appreciated.

Thanks!