Multiple SQL connection strings

Question

I have a winforms application & depending on the user selection regarding SQL authentication there are 2 possible connection strings :-

- using (var con = new SqlConnection(String.Format("Data Source={0}; database={1}; Integrated Security=True", Sql_ServerName, Sql_DataBaseName)))
- using (var con = new SqlConnection(String.Format("Data Source={0}; database={1}; User id={2}; Password={3};", Sql_ServerName, Sql_DataBaseName, txt_SqlAuth_UserName.Text, txt_SqlAuth_Password.Text)))

First one is for windows authentication with the second being a facility for entering a specific username/password for the SQL server (sa for example).

Apart from these con strings the remainder of the code is the same. How can I do an IF/THEN type statement depending on which selection the user has made??

I have attempted an IF/THEN & also declaring the var con in the variables block, both without success.

Any tips, pointer etc?