Viterbi detector is widely used in communication systems for signal detection. The exact performance of the detector is of research interest ever since the algorithm was proposed. Traditional methods to characterize the performance bound the bit error rate (BER) of the detector using error event analysis and minimum distance bounds. A Markovian approach was proposed to exactly characterize the performance of Viterbi decoder for convolutional codes. In this paper, we model the signal detection process for quantized ISI channels as a hidden Markov model (HMM) for evaluating the exact performance of the detector. We describe a procedure to obtain an exact closed form expression for BER of the detector for quantized ISI channels.