Criteria / guidelines for referring neuropathy foot patients to vascular surgery?

Signs of PAD/PVD. A diagnosis of neuropathy is not an absolute indication of a need for referral to a vascular surgeon. That referral would be based on objective findings and subjective complaints that could suggest the patient is also suffering from peripheral vascular disease or peripheral arterial disease. There are times when a patient with neuropathy may need a neurology referral to control their symptoms.
If circulation prob. Neuropathy does not cause vascular disease or circulation issues. The converse, however, may be true: that peripheral arterial disease (pad), or bad circulation, can cause neuropathy. I only refer to a vascular surgeon if a patient has signs/symptoms of pad, such as decreased pulses in the feet, abnormal noninvasive vascular studies (abis, or ankle-brachial indexes), or an abnormal angiogram.
No pulse. Certainly any one with absent foot pulses or an open ulcer that is slow to heal. Severe foot pain is often due to ischaemia rather than neuropathy.
Vascular. As stated well , that referral is based on the objective evaluation by your physician - whether that be your podiatrist or family doc . Neuropathy and vascular problems don't necessarily go hand in hand.