Different jurisdictions have different rules, but I’m confident in saying “yes” for all U.S. jurisdictions.
If the Defendant states that he was at a restaurant at the time of the murder, then it is legitimate to ask questions like, “Well, Mr. Smith testified that he saw you running from a dark alley where Joe’s body was found. Is he lying or mistaken?”
“So, Mr. Defendant, if you were at a restaurant across town, it is not possible that you were murdering Joe at the same time, is it?”
“Mr. Defendant, Officer Jones testified that the bullets found in Joe match the rifling pattern on your pistol. Was your pistol in your possession in the restaurant? Who else might have had access to it?”
“Mr. Defendant, is it possible that you left the restaurant, drove across town, killed Joe, and returned a short time later?”
I believe that these are all appropriate cross examination questions to a one question direct testimony that the Defendant was at a restaurant.
One thing that helps is to actually have counsel (ianal) who can respond to prosecution’s questions
How can the witness be expected to guess what goes on in Mr. Smith’s head?
This one would probably get knocked down if no mention of the murder was made during the testimony.
Again, if the testimony does not mention the murder, the prosecution cannot ask questions about it.
This is a leading question that would be disallowable, especially if the murder is not mentioned.
The subject of the trial is not valid for cross-examination in and of itself. If the defendant only testifies that he was in a restaurant from 7~9:00pm (previously established as the time of the murder), prosecution simply cannot ask about anything other than, say, what he ate, how nice the waitress was, etc., things that might reveal an inconsistency. But it really does help to have a lawyer to restrain the testimony.