Trulia's crime data is coming from www.spotcrime.com and it looks like a possible rolling 10 days of info.
My favorite site is www.crimereports.com which allows up to a 6-month search window
Note: Once you enter a property address go to the "Advanced Search" tab to select what type of information is important to you. Next, choose the duration of time you want to look at under "Date Range" (now limited to a 6-month view). You can also try these alternate crime reporting sites: http://tinyurl.com/a34pmyc
For schools, I suggest www.SchoolAndHousing.com
Based on property address, this site provides attendance area schools (Public, Private and Daycares) along with useful statistics and other information you should appreciate. They also have a cellphone mobile application, which is quite handy when you are viewing homes! Just access the website on your mobile phone to download the app. NOTE: Before making an offer on a property call the School District to CONFIRM the schools the property will feed to!