How to add multiple conditions on a single field in views?
So far as there is no support for nested groups in Drupal 7, we shoud do it slight differently. 

Join general filters (Published and Node type) in first AND group. May be we also should to add there "State IS NOT NULL" condition to exclude content with empty State field.

In second group we should place State = 'active' OR test = 'false'. This group - OR group.  In the Views admin interface in would be somthing like this: