Two men posing as utility workers looking for a gas leak killed a man and bound his wife with duct tape after being admitted to their home in an upscale Detroit suburb on Friday, the authorities in Michigan said.

One man, Carlos Jose Hernandez, 37, of Dearborn, Mich., was arrested after being stopped by the police in Shreveport, La., on Saturday, according to a news release from the Caddo Parish Sheriff’s Office. The other, whose name has not been released, was stopped and arrested in Plymouth Township, Mich., on Monday, according to a Facebook post from the Oakland County Sheriff’s Office.

Killed in the attack was Hussein Murray, 72, a business owner. His wife, also 72, was briefly hospitalized and was later released, according to the sheriff’s office. The woman’s phone and watch were taken during the attack, according to Karen McDonald, the Oakland County prosecutor.

The authorities said that the two intruders, in search of valuables, had first tried to talk their way into the home in Rochester Hills, Mich., about 10 p.m. Thursday but that the couple had not admitted them. The men indicated that they would return in the morning and then did so, Ms. McDonald said.

Footage of the Thursday night encounter released by the sheriff’s office from the couple’s Ring camera shows a man who the authorities said was Mr. Hernandez at the couple’s doorstep in a yellow vest and a mask and holding a clipboard. The other man, also in a yellow vest, stands facing away from the camera.

In the video, the man the authorities identified as Mr. Hernandez says they are with DTE, an energy company based in Detroit, and turns his clipboard toward the camera to show a form with the DTE logo.

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