TexasCHLforum.com

Generally, peace officers can arrest for an offense if it is committed in their presence, without a warrant. There are some other provisions, example under circumstances and in a place where it is reasonable to believe a felony has been committed, etc and for specific crimes, violations of protective orders etc. These are all spelled out in the Codes. "Have you arrested" usually means that someone provided specific facts to a peace officer.

Assuming the officer does not witness the crime, someone had to have done so and reported that to an officer. The facts reported must be reasonably accurate, which means you had better hope the officer writes them in his report the way you reported them. I reported the theft of a cashiers check, which had not been endorsed, to the District Attorney many years ago. The investigator wrote in the report that the check had been endorsed, a critically important circumstance. The woman who had received the check was unceremoniously arrested and hauled off to the hoosegow, strip searched etc, processed through like a common criminal, and I had to fight the subsequent malicious prosecution action. It all worked out OK eventually but was expensive, worrisome and unpleasant.