I was wondering about the same issue yesterday, but think I understood what was going on, thanks to a powerful reply of Geoff in the topic "The Ring" (which paved the way and helped me to connect some dots):
"Both BOB and MIKE have a relationship with personal artifacts from their victims. MIKE used Teresa's ring, BOB used Laura's half-heart necklace. I would venture to say that in the convenience store scene, MIKE is gloating about his relationship to Teresa Banks as though it were a marriage. Mrs. Tremond's grandson tells both of them to "fell a victim," and I think they both had in mind Teresa and Laura, respectively. When BOB kills Teresa, I think it angers MIKE (and possibly other lodge spirits) because she was supposed to be MIKE's victim or future host or whatever. This comes from the "You stole the corn... I had it canned... over the store" line during the traffic jam scene.
I think the Banks murder is what happened to cause a figurative rift between MIKE and BOB, perhaps leading MIKE to see "the face of God," and literally divide into the Gerard-entity and Little MIKE, the representation of "the arm," or MIKE's link to BOB and the killing partnership they had."
The green "owl" ring somehow connects the wearer to MIKE.
I firmly believe that after Teresa Banks death Deputy Cliff Howard stole the ring. After all, this is obviously the only reason Chet Desmond returns to the trailer park with the intention of searching Deputy Cliff's trailer (Irony, he doesn't seem to find the ring but the ring finds him).
I'm also convinced that Deputy Cliff tried the ring and put it on his finger - thus making a connection with MIKE (the extent of the connection remaining unknown).
Now Laura has already "access" to the spirits of the Lodge. I'm certain she has never met Deputy Cliff Howard but instantly and empathically recognizes him as "MIKE".
That's it - from my point of view.
Where it really gets complicated is THIS: Deputy Cliff draws his gun.
Was he actually trying to kill Bobby (who was there with a witness he would have had to shoot, too)? Kill the reliable Twin Peaks High School drug messenger? Where is the logic in that?
OR
Was he (MIKE) trying to kill Laura to get even with BOB? Or was he trying to kill her (because she wanted to die) to prevent BOB from posessing her?
And then Laura's reaction: Was she laughing or was she hysterical, now that Bobby Briggs had taken her chance to get killed and end her suffering?