By hysterectomy I would assume that you mean a total hysterectomy in which the whole uterus and cervix is removed as opposed to partial or subtotal hysterectomy in which the cervix is left intact. Cervical screening would only be an option in case of partial hysterectomy. STDs can infect women regardless of the presence or absence of a uterus, because the STD infections often stay in the body and blood without producing symptoms. So practising safe sex is still the best approach to take when having sexual relations.
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