Safety and security in Padua is always a welcome sight for tourists. Padua's notoriously tense crime situation is not common in Italy's big cities. The city is relatively small, so security is almost idyllic. It's hard to say what the dangerous parts of Padua are.
You should be a bit more careful around the railway and bus stations. You may fall victim to pickpocketing, other petty theft or fraud, but not as often as in bigger cities. Teenagers are more likely to commit such offences.
If you contact the police, issues are resolved very quickly. Therefore, tourists only need to adhere to basic safety rules.