I am a law student and resident of CA. I worked in DC this summer for a paid internship and claimed CA as my state (it showed up on my W-2 for this employment as well). Do I need to file both a CA and DC tax return?

No. DC has no nonresident state income tax filing requirement so you will only need to report your DC-sourced income on your CA resident state income tax return.

You are not required to file a DC return if you are a nonresident of DC unless you are claiming a refund of DC taxes withheld or DC estimated taxes paid. Use Form D-40B, Non-Resident Request for Refund (available by visiting http://otr.cfo.dc.gov/node/379192).