The BBC are bound by their editorial rules on using trusted sources. One of which is the police.
But who decides the police are "trusted"? Because they clearly can't be on this. It is known that they repeatedly lie.
The absolute minimum would be to clarify on every repetition of a police statement - if you have no other information - that the police say it's a "woman", but the actual sex is unknown, as the police do not base "man" or "woman" on sex.
Suggestion:
"The police described the accused as a "woman", but their policies base this purely on an arrestee's choice, so this does not mean the accused was actually female. Other information to confirm the accused was female was not available.
"Statistically, females rarely commit this sort of crime, so the possibility of the accused being male is quite high - in the last X years Y% of "women" convicted of Z were male."
That would be informing your readers. Although it would also highlight a failure to actually locate the truth.