ODBC connection with windows NT authentication

i am making application inwhich sql server 2008 database is install on windows server and shared the database on network. The Client PC connected with the database through ODBC , making a connection. When I try to connection on ODBC through login sa , password . It connected successfully. But when I try to connect with windows NT authentication, it did not make connection. why? I want to connect Client PC to database through ODBC with windows NT authentication mode how do it ?