According to this article from the CDC, "People who enjoy outdoor activities where freshwater or wet soil are encountered may be at risk for leptospirosis. This includes swimming, kayaking, rafting and canoeing in freshwater, hiking and camping."
There is no mention of activities like running and walking in an urban setting, so that brought up worries in me about that possibility, considering it's quite common for people who practice these types of activities to do it in the rain.
Updated: My main worry is in regards to puddles that might form in the curbs or sidewalks, either exposed or hidden under loose blocks that form some sidewalks.