In this paper, we consider the behavior of an autoregressive (AR) detector for partial-response (PR) signaling against offtrack interference (OTI) environment in perpendicular magnetic recording. Based on the behavior, we derive the optimum branch metric to construct the detector by the Viterbi algorithm. We propose an optimum AR detector for OTI that considers an optimum branch metric calculation and an estimation of noise power due to OTI in order to calculate an accurate branch metric. To evaluate the reliability of soft-output likelihood values calculated by our proposed AR detector, we demonstrate a bit error rate performance (BER) of low-density parity-check (LDPC) codes under OTI existing channel by computer simulation. Our simulation results show the proposed AR detector can achieve a better LDPC-coded BER performance than the conventional AR detector. We also show the BER performance of our proposal can keep within 0.5dB of the case that perfect channel state information regarding OTI is used in the detector. In addition, we show that the partial-response maximum-likelihood (PRML) detector is robust against OTI even if OTI is not handled by the detector.