How did Connie know Michael killed Carlo

It seems she found out way later. Obviously she came straight back from Vegas for Carlo’s funeral. Then who knows how much longer after the funeral they are packing up the house to move to Nevada when Connie comes storming in accusing Michael of Carlo’s murder.

Surely they had some kind of story cooked up to tell Connie that either Carlo died by an accident or was murdered by other mobsters, etc. How did she just suddenly know it was Micheal?
Does the book go into further explanation about this?

Maybe I'm wrong, but I think that they just messed up the continuity. I think the altercation is supposed to occur within a few days of the hits. The hits on the dons make the newspapers, then Carlo doesn't show up in Vegas and before too long Connie figures things out (she's a Corleone, too) and flies back home. The moving van and packing up the house seems out of sync, and in the novel that actually does occur later.

According to the movie,the hit on Carlo occurred on the same day as the killing of the other Bosses.
After he tells Carlo that Barzini, Tattaglia ,Cuneo, Stracchi, and Greene are dead, he says "Today I settled all Family business"..

I agree with Pete that the altercation happened very soon after the hits.

Remember, Connie picks up a newspaper and tells Kay "Read the papers. Read the papers." I'm sure she was referring to the coverage of the killings of the other Bosses (although probably not Carlo, who I'm sure was never found).

That wouldn't have made sense had there been a long time between the killings and Connie's confrontation with Michael.

The altercation with Carlo,followed by Carlo's murder, took place on the very day of the hits.

Connie was with Carlo, not in Vegas, after the baptism, when Michael told him he couldn't go to Vegas. There was no way Carlo could have had a funeral, after being murdered by garotte, with a big red circle around his dead neck. His body would have disappeared, as do most Mob victims' bodies in important hits. Carlo was killed the same day as the Dons but the moving vans would have started arriving arriving very soon after that.

Don't know he told Carlo There's a car waiting for you outside to take you to the airport. I'll call your wife, to tell her what flight you're on like she had gone ahead and was already in Vegas

I reckon Connie's return and confrontation with Michael, happened within a couple of days after the hits

no rocket science! Michael! You lousy bastard -- you killed my husband! You waited until Papa died so nobody could stop you, and then you killed him. You blamed him for Sonny -- you always did. Everybody did.

I too reckon, the moving van and packing up the house would have already been arranged as they knew they were leaving

Outside the Church after the baptism
Doesn't Kay “Read the papers -- read the papers!” That Newspaper must be at least a couple of days old!!

Maybe I am misunderstanding but it seems to me, too that "she [Connie] had gone ahead and was already in Vegas"
ie: Connie was not with Carlo in New York

Besides Michael's right hand man in Nevada! - wasn't Carlo phoning his mistress? when Michael walked in

Yes, you are misunderstanding: Connie was not "already in Vegas ie: Connie was not with Carlo in New York."
Connie was in the church with Carlo, Michael and Kay. Connie was right behind Carlo immediately after the baptism:. Carlo was killed the same day as the baptism, There is no way she and her children and their household could have gotten to Vegas before Carlo was killed. Most likely, she would have waited at the Mall until Carlo was "released" to go to Vegas.

I don't think that this is right, TB. Michael gives Carlo a ticket and a car to the airport, and says he'll call Connie and tell her what flight Carlo is on. That all implies that Connie has gone on ahead.

The way I see it is that "the first vacation together" Connie mentions is the first time everybody - Michael and Kay, Connie and Carlo, Mama - are traveling together. It's a big deal for Connie because she thinks the baptism has lifted the cloud of suspicion over Carlo. Apparently they're all leaving direct from the church, but Michael holds back himself and Carlo and sends the others ahead. He has to clear the mall because Tessio and Carlo will be dealt with there.

Again, none of what I'm saying makes sense with the moving van and Kay standing there packing when Connie runs in. In the novel, those are distinct events months apart, and I don't think Coppola merged them rationally.

I too don't think that TB is right, in this instance
That was no misunderstanding: "she [Connie] had gone ahead and was already in Vegas" as per Michael's plan all along

No doubt Connie was in the church She is the mother of the baby being baptized!
She was holding the baby outside the church and even got the baby's new Godfather Michael to kiss him certainly thinking and hoping the baptism has lifted the cloud of suspicion over Carlo.

Exactly Pete he sent Mama and Connie ahead, on "the first vacation together" because He has to clear the mall, to settle all Family business That was his strategy all along He played this one beautifully

Michael: Carlo -- can't go to Vegas Something's come up Everybody's going to leave without us

If Most likely, she would have waited at the Mall until Carlo was "released" to go to Vegas where was she
1. when Michael walked in
2. Carlo was answering for Santino
3. he was getting into the car, to take him to the airport
4. also why would she come to confront Michael, in the car instead of just walking over?

As regards the moving van and Kay standing there packing when Connie runs in, I reckon a couple of days have passed after the hits, so it makes sense in the movie that the relocation was progressing full swing