A leech attaches itself when it bites, and it will stay attached until it has had its fill of blood. Due to an anticoagulant (hirudin) that leeches secrete, bites may bleed more than a normal wound after the leech is removed. The effect of the anticoagulant will wear off several hours after the leech is removed and the wound is cleaned. The amount of blood loss from a leech bite is more of a nuisance than a danger for humans.
Leech bites tend to itch while healing, but this is normal. Itching is not reason for alarm, although the wound should be watched to ensure it is healing and to make sure there are no signs of infection.
Leeches do carry parasites in their digestive tract, but these cannot survive in humans and do not pose a threat. If the wound is cleaned, there is no more risk of infection than any other small wound. The wound should not be scratched as this may complicate healing and introduce other infections.