Technically the cops were committing Criminal Trespass by going into the backyard of a private residence without permission.
They will say they had every right of course, but I think they lost that right when they neglected to knock on the door and announce who they were.
If you loudly knock on the door and yell "POLICE OFFICERS" then get no response, then by all means check out the back of the house.
In Texas Breaking and Entering is called
Criminal Trespass.
The next "stage" above that is Burglary.
Criminal Trespass would be going onto/into someone's property without permission and
this includes people's yards.
It also includes getting into property by using deceptive methods, like saying your the cable guy/gal or pretending to be a cop or pretending to sell something etc....
You do not have to break anything to be charged with criminal trespass. If a stranger is sitting in my backyard that's criminal trespass. If my door's unlocked and someone walks in and sits on my couch that's criminal trespass.
Even if the person leaves immediately you can still fill out a police report but use your best judgement on it. Only a very vindictive person would file charges just because a person walks across their yard a couple times, and LE wouldn't be thrilled with that
.....2 Cents......
In Texas, breaking and entering is known as criminal trespass:
What Exactly Constitutes Breaking and Entering?
Texas Burglary and Criminal Trespass Laws - FindLaw
I disagree.
The cops were not "criminally trespassing."
Using your example of someone sitting in your backyard, They are not criminally trespassing either.
In order to be criminally trespassed in this example, you (the homeowner or manager of the property) would have to tell them to leave, or have the cops tell them to leave. If they return, they can be arrested for criminal trespass. The cops do not have authorization to tell that person directly to leave. You have to or have the cops tell them .There are some cities that use an affidavit that's filled out before hand, and gives the cops authorization to remove someone from private property, but even then the cops have to tell you to leave first. If you return, you can be arrested.
There are situations where someone can be arrested without being told to go first.
If the property is posted with signs.
If the property has a fence that would be used to keep people out.
Painted markings a certain distance apart.
There were no signs here.
There was no fence.
There were no markings.
In this case, because he was a cop responding to a call, he's allowed to enter this property even if it was posted.
There are other reasons a cop can enter private property.
If they are chasing someone that has committed a crime.
If they have to report a death to a family.
In the OJ Simpson case, the cops scaled his fence without getting a call and without a warrant. They said they feared someone's life inside the house may be in danger.
The attorneys tried to suppress all evidence that they found in the house, but the court allowed it.
Texas Penal Code § 30.05 | FindLaw
In order to be criminally trespassed, in your example of someone being inside of your house, there would be a need to show intent of committing a crime. So yes, if someone breaks into your house, it would be reasonable to assume they have/had the intent of robbing you.
Here's an affidavit that Dallas uses for criminal trespass. I'm not sure of Forth Worth has one or not.
https://www.dallaspolice.net/divisions/Shared Documents/SE_Criminal_Trespass_Affidavit.pdf