How to check connection string in SSMS2012?
Within SSMS, I'm not sure there's an easy way to do that.  But a simple query will return you the information (without the password of a connection string, obviously):

select
    'data source=' + @@servername +
    ';initial catalog=' + db_name() +
    case type_desc
        when 'WINDOWS_LOGIN' 
            then ';trusted_connection=true'
        else
            ';user id=' + suser_name()
    end
from sys.server_principals
where name = suser_name()


Note, db_name() will return the current database name if there is no parameter specified, so that is dependent on your current scope.