Basel is a very peaceful city, relative to it's size. The rate of criminality is very low according to international statistics. Even single female travellers, who enjoy nightlife will feel secure long after midnight. Basel folks are very helpful. Most of them  speak english. For your safety, I mention just the pickpockets, who might cause problems when the city is crowded during carnival or atumn fair

For the worst case, please note the emergency telephone numbers: 

117: Police ("Polizei")

144: Emergency medical help ( "Sanität")

118: fire brigade ("Feuerwehr"

 The staff on the phone speak english. Just tell them who you are, where you are, and what problem you have.

If you need help in the street, just shout "Help". We will understand and help. Be sure! But, as I said, it is very unlikely that you will be victim of a criminal act.

 Other useful numbers:

SBB rail service: 0900 300 300 ( Hotline /  Francs 1.19 per minute)

Basel Tourism board: 061 268 6868