Police have named the man shot dead as karate instructor Chris Brown, 29. Samantha Stobbart, 22, was injured.
Pc David Rathband, 42, was shot in Newcastle on Sunday morning and is in a critical condition.
All armed officers in the region have been deployed, and officers have been called in from other forces to aid the search.
Before the attacks began Moat's Facebook status was changed to read: "Just got out of jail, I've lost everything, my business, my property and to top it all off my lass has gone off with someone else.
"Watch and see what happens."
Murder in the Time of facebook