It's the same place under State & Local > Other > MA Schedule HC. So long as the insurance your client had met the MCC, why should it matter whether it's private?
Ah, I think what you're looking for is the provider info.
If that is the case, on the same input screen for Sch HC, you'd find a blue hyperlink in the top right corner in tiny prints for Provider. Click on that and it'll bring to to the input screen for insurance provider.
That's a typical setup in ProConnect Tax. Very often, additional details are to be entered using the link in the top right corner.
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