There are only two ways to connect to SQL Database:
1) Using SQL Password where you need to specified the credentials
2) or using domain authentication, where the credentials are same as you logged in your pc:
Option 1: Data source=localhost; initial catalog=master;trusted connection = true
Option 2: Data source=localhost; initial catalog=master;Integrated security=SSPI
But you can check the following link where you will find any connection string to most databases and all variants of connection:
http://www.connectionstrings.com/
Regards.
Majahide
solved Access a database without a password? [closed]