Is it permitted to inform the police on a thief, seeing as the authorities will place the thief in jail – a punishment that goes beyond the Torah’s punishment for a thief? I saw a responsum in Igross Moshe (Orach Chaim Vol 5 no. 9) that seems to prohibit this, and a responsum of Rav Elyashiv (Kovetz Teshuvos Vol 1 no. 198) that permits it. Is there a dispute?
The responsum of R’ Moshe Feinstein that you quote lacks details of the circumstances involved, and as such it is difficult to draw conclusions.
The correct approach is spelled out by the Maharshal in Yam Shel Shlomo (Bava Kamma 3:6), cited in Shach (Ch M 4:5). If one has the opportunity to recover a stolen object via Beis Din one may not go to the police, and he if nonetheless does so he will be liable for any damage that the thief suffers above and beyond what the Halacha proscribes. This is because such action classifies him as a moser – a very serious aveiro – and a moser must pay damages suffered. However, if there is no other way to recover the theft he may inform the police and he will not have to pay for any excess damage caused to the thief, since he is permitted under the rules of Ovid Innash Dinna Denafshei.