Jose Gilberto Rodriguez, 46, of Illinois, was previously convicted in a series of crimes dating back to 1986.
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Records show Rodriguez was convicted for burglary, attempted aggravated sex abuse, auto theft, and criminal trespass.
Rodriguez was sentenced to 20 years for the sex offense involving a 16-year-old female, and 25 years for burglary of a habitation in 1990.
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Classified as a "high" risk-level sex offender, Rodriguez was released on parole in September 2017.
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He was last registered with the Dallas County Sheriff's Office in December 2017.
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In a joint news conference Monday evening, Houston police and the Harris County Sheriff's Office linked Rodriguez to the Mattress One murder, the murder of a female worker Saturday at the Mattress Firm near Willowbrook Mall, and the killing of a 62-year-old widow in Cypress last Friday.
Authorities say Rodriguez is considered armed and "extremely" dangerous and urge those who encounter him to not approach him and contact police immediately.
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