Hidden Markov Model for Speech Rcognition. HMM Number of States
The dimension of the frame's feature vector N depends on the frequency range and the number of frequency bins in the frame. For example for 16khz audio signal it's common to take 39 feature vectors created from 40 cepstrum values. For 8khz it's enough to have 20 cepstrum values.

Feature dimension is not equivalent to the frame length. Frame length could be rather arbitrary as long as you catch sound variation in time. Frame length is determined by how fast your speech signal changes. It's enough to have 10ms frame length, though 20ms and 5ms work almost equally well. If you have frame of 30ms you will have issues since some speech sounds change faster. Thrilled r for example.

Number of distinct HMM models (tied phone detectors for example) depends on the diversity of the speech signal, on the number of distinct sounds (temporal audio patterns) there. Each distinct sound ideally has to be better modelled with it's own HMM model. The number of states depends on the size of the training database and on the vocabulary of the database, not on the feature extraction parameters. The more words you want to recognize the more HMM models you need.

There is no direct relation between both feature vector size and length of the frame and the number of states in HMM models.