This is a civil case, not a criminal one. His 5th amendment protections are much weaker. If he says that his testimony may support criminal charges, then he is allowed to take the 5th. However, in a civil trial, the fact finder is allowed to draw a negative inference from that.
Having said that, none if this is relevent. He already testified during the State's case, which is the only time he would need to invoke privilege. Since this is the defense case, they get to simply not call him.
Unless one of his co-defendants subpoenaed him, which is also not the case.
I actually read the 7 page opinion, because normally there is at least some shred of reasonableness in these crazy opinions. But this one ... those 7 pages have nothing.
I'll just leave this little nugget from the end:
The really telling part of all of this is that there was no reason for this to be a thing. The state attorney general chose to fight this specific case. Then chose to send a letter to every hospital saying the injunction did not actually protect them, and chose to appeal the decision to the state Supreme Court.
None of that had to happen. He could have let the extreme cases go through while fighting to remove women's rights on the more "controversial" cases, but instead chose to make a test case out the most extreme interpretation of his extremist ideology.
Despite this, the court seems willfully blind to the fact that the reason for needing an injunction is that the state is acting in demonstorable bad faith.
Side note. Remember when the US SC ruled that this law could not be challenged because the state was not going to be the one enforcing it?