According to the Galveston County District Attorney's Office, Ghose was detained at a border checkpoint near New Mexico yesterday.
Ghose, 41, has been arrested and charged with murder in the late Wednesday shootings.
His bond was set at USD 150,000.
The shooting was reported around 9 pm (local time) at a house in the 700 block of Mayhill Ridge Lane, during an argument between Ghose and the two residents, police said.
According to the League City police, officers found the body of 43-year-old Clarence Wayne Harris II, who had been shot several times, lying in the driveway in front of the house.
Police said Amanda Harris, 36, was also found suffering from a gunshot wound, and was taken to a local hospital for treatment.
According to the police, Ghose was present during a party at the couple's house. But at some point of time, they had an argument with him, leading to the shooting.
In an affidavit, Amanda said, she called police shortly before 9 pm (local time). She told police that she was going to make a citizen arrest because her ex-husband, Ghose, was at her doorstep.
Amanda also alleged that Ghose had been stalking her for years. Apparently, she, and her husband, both had weapons on them.
The police officer on the line heard her scream, "Get away from my gun!" and then additional screams and yelling in the background. Shots also began to fire off in the background.
Ghose allegedly shot at Amanda's husband, Wayne, after an argument broke out between them, in front of the house.
The police said in a release that Ghose had already left the home before they could arrive.
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