This will be rather tricky, as prior to 1660s with the formal recognition, Connecticut enjoyed a quasi-independence in terms of internal matters, so its main body, the General Court ( Granted by the Massachusetts General court in the 30s ), who had the executive, legislative and judicial function, and since 1640s, the Particular court, and "inferior" town courts, during this period, only the General court had the jurisdiction of matters concerning life and appelate jurisdiction. Town courts only had jurisdiction of its own inhabitants, of matters concerning trespasses and debts up to 40s, with Particular court the rest except capital crimes, limb or banishment.

Only since the 60s, when the hierarchy was more concretely established, from local/town, to county, to Court of Assistants ( which had the jurisdiction for capital crimes, granted by the General court ) to the General court.

As for the trials themselves, one would need more information to say anything substantial, but relying on common law as practiced in Britain at the time might not be that helpful to establish such a thing. So with this little information, the only thing I can say is that in 1642 Capital laws, witchcraft was one of them, which read:

If any man or woman be a witch - that is, hath or conculteth with a familiar spirit - they shall be put to death.

As far as I know, there is no extant document about Alse Young, Mary Johnson was doomed by her own confession, and then we are already in the 1650s, but going by case law and statutes, spectral evidence was admissible at the time, as well as in Britain^(1), where the issue was not of admissability, but whether it constituted proof. Naturally, more can be said, specially to specific follow-ups.

1.Trials of Amy Duny and Rose Collender in 1662, Suffolk.