This type of centipede doesn't bite, as far as I know. There are however other kinds of centipedes (not house centipedes like this one) that bite, which can hurt a lot.
Quotes from wikipedia:
Some species of centipede can be hazardous to humans because of their bite. Although a bite to an adult human is usually very painful and may cause severe swelling, chills, fever, and weakness, it is unlikely to be fatal. Bites can be dangerous to small children and those with allergies to bee stings. The bite of larger centipedes can induce anaphylactic shock in such people. Smaller centipedes usually do not puncture human skin.
The history of a centipede bite is fairly straightforward; the victim typically sees and identifies the characteristic centipede before, or soon after being bitten.
Symptoms which are most likely to develop include:
severe pain, which is usually in proportion to the size of the centipede
swelling and redness
swollen, painful lymph nodes in the regions of the bitten limb
palpitations or a racing pulse
nausea and vomiting
local itching and burning sensations
The wound left by the bite may be accompanied by swelling, redness, and small puncture wounds which may form a circular pattern. This wound may be susceptible to local ulcerations and necrosis.