Can parliament summon people to give testimonies? Or, alternatively, could this go to court? Because we're at a deadlock at this stage. His word vs Rafiq's.
Some thing to clear up...
The witness statement we are digesting is not a submission of evidence to Parliament per se. It is the submission of evidence for his employment tribunal, which Rafiq has voluntary submitted to Parliament to support his claims in oral evidence to the DCMS select committee and which that committee has taken the highly unusual (I worked in Parliament for six years) of publishing in full in advance today, on the select committee website. Usually they would wait till they'd gathered all the evidence then publish it all collectively, alongside their report. Their report is yet to come of course - so that will have the suits in the ECB shaking, as recommendations will be incoming. They will probably steer clear from Yorkshire, other than to say whether they agree with the institutional racism allegation, because Yorkshire are subject to legal proceedings anyway. Plus Parliament's job is to go after regulators and reform them; to make suggestions as to what should happen to prevent it occurring again.
The witness statement is therefore already part of a legal process - it is a submission to an employment tribunal, which is a court. Rafiq is already by definition happy to stand on them in court, as part of his tribunal v YCCC.
Can parties bring legal proceedings against Rafiq? No. No proceedings are allowed to be given against evidence submitted to Parliament under parliamentary privilege rules. He's protected. However, given the high profile nature of the case, I would be amazed if Parliament has been gung ho about allowing DCMS to just publish that without lawyers pouring over it as so many very high profile people are named that if it were wrong, then the whole constitutional idea of parliamentary privilege would be rightly called into question. And that would, constitutionally, be a big deal.
If those claims are repeated outside or Parliament as facts not allegations, they can be viewed and contested as libellous. Hence why links of that, other than the Parliament one which is protected, aren't being hosted anymore by media organisations - unless I've missed it, they've largely been taken down.
But, I mean, if he's submitting that to an employment tribunal, he's probably got all sorts of receipts. That's a type court, he can have it thrown out and - I think (I know Parliament, I'm not a lawyer) - probably be then sued? I think it's pretty likely he's going to win, personally in his case v YCCC specifically.
To answer the question: Parliament does summon people to give evidence to select committees, but they don't have a legal power to do so like they do in the US, for example. You can't be forced to do it. In practice, nearly every one does - even Rupert Murdoch showed up for a four hour shit-kicking on phone hacking. Zuckerberg dodged it once, I think - not many do.