I hate to resurrect a thread a while back which talked about whether Connie knew about Fredo's murder.
But today it suddenly occured to me that Kay alread knew the murder at the start of Part III and that Vincent also knew about it. It would be very natural for Connie to know it was a murder then.

I don't beleive that Connie was in on the plan to kill Fredo. She knew absolutely nothing about that plan. The family was told that Fredo drowned in a boat accident while fishing.

However I do believe that eventually Connie (as well as a few others who were "inside" the family), came to realize that Michael ordered the death of his own brother. Carefully read the exchange between Connie and Michael in GFIII where Connie and Mike are talking on the balcony and Connie is preparing Mike's insulin shot. More importantly, to get a better feeling, watch the scene when you get a chance.

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MICHAEL: I made confession, Connie. I confessed my sins.

CONNIE: Why Michael, that's not like you. You don't have to confess your sins to a stranger.

MICHAEL: It was the man. A good man. A true priest. He changed things.

CONNIE: Michael, you know, sometimes I think of poor Fredo, drowned. It was God's will. It was a terrible accident. But it's finished.

(then, after Michael sighs)

Michael, I love you. I'll always help you.

<They hug. Connie starts crying and Michael comforts her.>
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Now all Michael says was that he went to confession and that the Cardinal was a good priest who changed things. And what does Connie bring up to him? Fredo's death. Almost as if she knows that Michael was struggling with his own guilt in having Fredo killed and that is why he needed to confess to Lamberto.

It was as if Connie was really telling Michael "Don't worry about it, I don't hold it against you, it's finished, let it go, it's over with and I love you anyway."

Why would she bring up Fredos death unless deep down inside she knew that Michael had him killed and that Michael was struggling with guilt. She attempts to ease Michael's conscience with her reply.

Even Mary and Vincent know about it,Kay says"Anthony knows you killed Fredo".How did it get out in the open?

Anthony was supposed to go fishing with Uncle Fredo when Connie took him out of the boat. Although he may not have understood the implication of the boat returning without Fredo, he certainly could have put the pieces together when he was older.

I don't think Mary knew about Fredo's murder. She had a blind love for Michael, the type of love that only a very spoiled and sheltered daughter could have for a father.