Sorry OP, I've only just seen this. The stats that have been debunked are the fake stats put out by transactivists about a supposed high suicide rate etc.
The genuine stats about TW crime are coming out slowly. TW offend at the same rate as other males, which is much higher than the female crime rate. Transitioning does not reduce a male person's likelihood of committing a crime. Refs: Sexton et al 2010; Dhejne et al 2011.
TW seem more likely than other males to commit sexual offences, according to official statistics. (This is one reason why women don't want them in places where we are likely to be undressed or vulnerable.)
The Ministry of Justice stated in January 2022:
As of our latest data collection on 31 March 2021, there were 146 transgender women (that is, prisoners who were legally male and identified as female) in all prisons across England and Wales. ... These figures do not include transgender prisoners with gender recognition certificates ...In the men’s estate, there were 87 transgender women with a conviction for at least one sexual offence.
questions-statements.parliament.uk/written-questions/detail/2022-01-06/98878
So, 60% of self-identifying TW in prison have committed sexual offences, compared with about 17% of all male prisoners, according to Ministry of Justice figures.
Some of these TW are housed in women's prisons, despite having committed serious offences against women and children.
From the Keep Women's Prisons Single-sex campaign:
kpssinfo.org/males-in-womens-prisons-convictions-sentences/
We have collected details of 28 males convicted between 2014 and 2020 who are known to have been held in women’s prisons or have been given a place in a women’s hostel after release. However, the true number of males who have been held in female prisons is almost certain to be higher than this. ...
All but two were convicted of violent or sexual offences. This includes: ten who were convicted of rape or attempted rape, including the rape of children; ten who were convicted of murder or attempted murder; four who were convicted of sexual offences against children.
transcrimeuk.com has a long list of transpeople who have been convicted of crimes. Most are by TW, but in many cases these have been recorded as crimes by women.
And there's masses more information available. This is just a start.