In Texas, an officer can only make forced entry to execute a felony arrest warrant. They can get someone to open the door and then force their way in or, if necessary, they can kick the door in.
For a misdemeanor arrest warrant they can only enter if someone with apparent authority lets them in. An officer cannot make forced entry on an arrest warrant for a misdemeanor warrant. If a person answers the door and tells the officer that the suspect named in the misdemeanor arrest warrant isn't there, than yes the officer has to take their word for it. The officer cannot enter without permission just based on the warrant. However, if it is determined that the individual lied to hide the suspect than that individual can be charged with hindering apprehension. Also if the officer sees the suspect in the premises or knows he/she is there and commands him/her to exit so that they can be arrested on the warrant, than the individual can arguably be charged with evading arrest for not doing so. I actually successfully prosecuted someone for doing that.
The exception for a misdemeanor arrest warrant is if there are exigent circumstances that evidence will be lost or destroyed. If an officer is executing a misdemeanor arrest warrant and sees that the suspect is running to the bathroom with the drugs he was suspected of having, than it may be permissible for the officer to make a forced entry. But if it was suspected that the suspect would be in possession of evidence than the warrant probably would have been a combination search and arrest warrant, so the officer could have made forced entry anyway.