The instructions provided in the document below will help you find detailed Census data for your legislative district.
To build your profile, begin at the American FactFInder advanced search page. One of the datasets you'll use is the American Community Survey; the ACS provides ongoing statistical sampling of the U.S. population between the Decennial Censuses. ACS is an excellent resource for updated local data.
In addition to using the Census and GIS tools described on this page, consider the following:
Oliver is a mapping tool provided by MASS GIS for displaying data at a variety of geographic levels, including legislative districts.
This PowerPoint presentation shows some of the specialized district maps that may be created using the Oliver mapping tool.