Jose Gilberto Rodriguez, 46, of Illinois, was previously convicted in a series of crimes dating back to 1986.
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.
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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