Marcus Evans shared video of the incident on Facebook.
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It shows the officer with one hand on the steering wheel and the other one on her phone.
Chief Charles F. Kimble says the complaint is under review.
"The Killeen Police Department was made aware of a video circulating on social media that depicted a Killeen police officer driving a marked patrol unit with allegations that the officer was not wearing a seatbelt and was texting while driving," said Chief Kimble in a statement. "Although, both of these violations are minor in nature, we understand that the expectations that our community expects were not met in this incident."
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Chief Kimble says he's thankful to the public for bringing the incident to his attention.
Texting while driving is prohibited under Texas law and drivers are required to wear seat belts, according to the Texas Department of Transportation.
"We take traffic enforcement and safety seriously and will handle this matter the same," said Chief Kimble.