Texas Code of Criminal Procedure Article 14.04 has four basic requirements that must be met to make an arrest without a warrant for an offense not committed within the presence of an officer:  (1) the person who gives the information to the peace officer must be credible; (2) the offense must be a felony; (3) the offender must be about to escape; and (4) there must be no time to procure a warrant.

A police radio broadcast and telephone messages from out-of-state authority may provide the basis of an arrest under this section.
The legislature has written this law very specifically, and largely out of 4th Amendment protections against unreasonable search and seizure as written by the founding fathers.  There is an strong preference for a warrant to be obtained prior to making an arrest.  If an offense is committed in the presence of an officer, and the officer believes he has probable cause to believe that someone committed it then he can make an arrest without a warrant.