There is video of the passenger -- identified as Samantha Broberg, 33 -- falling overboard.
In a statement Saturday evening, the Coast Guard outlined its efforts: "Coast Guard aircrews continued searching through the day and into the evening Saturday, after beginning a search Friday for a woman who fell from a cruise ship about 200 miles southeast of Galveston, Texas...Coast Guard HC-144 Ocean Sentry airplane crews from Aviation Training Center Mobile, Alabama, and Air Station Corpus Christi, Texas, have alternated sorties since beginning the search, saturating a 22 by 63 nautical mile area with a combined search area total of more than 3,000 square miles.
The statement added, "The Ocean Sentry aircrews have stopped searching for the night and plan to resume at first light Sunday."
The Coast Guard also confirmed that there was indeed video of Broberg falling overboard: "She was not found aboard the ship, but they reported that video showed her falling overboard from the 10th deck at around 2 a.m. After it was confirmed that she had fallen overboard, the crew contacted the Coast Guard at about 5 p.m," the statement read.
Initially, on Friday, the Coast Guard said in a statement, "Watchstanders with the 8th Coast Guard District command center received a call from the master of the Carnival Liberty stating that they had a video of a woman falling overboard around 2 a.m., and that they conducted an accountable search for all passengers. Broberg was found to be missing. The watchstanders directed the launch of Coast Guard Aviation Training Center Mobile, Alabama HC-144 Ocean Sentry aircrew to conduct a search for Broberg."
The woman's family released a statement Saturday asking for privacy.
"We hope and pray the U.S. Coast Guard is able to bring Samantha home," the statement said.
Passenger Linda Lopez told ABC station KTRK-TV in Houston of the ship's staff, "They wanted to check every single room to make sure that every guest was in their room. They were just keeping up updated like 'we have not found her.' People are talking about it everywhere. They're very sad."
In a statement Friday, Carnival said, "Earlier today, a 33-year-old female guest on the cruise ship Carnival Liberty was reported missing by traveling companions. A ship-wide search was conducted along with a review of the ship’s camera footage. Unfortunately, it appears the guest may have gone overboard early this morning. Authorities were notified including the U.S. Coast Guard which is initiating a search effort in the area where the ship was located when the individual was last seen."
Carnival added, "Carnival’s CareTeam is providing support to the guest’s traveling companions and family. We are keeping our guest and her loved ones in our thoughts during this difficult time. Carnival Liberty departed Galveston, Texas on a four-day Mexico cruise on Thursday. The ship is based in Galveston year-round."