Searching through existing repositories for a specific mobile app screen design is currently either slow or tedious. Such searches are either limited to basic keyword searches (Google Image Search) or require as input a complete query screen image (SWIRE). A promising alternative is interactive partial sketching, which is more structured than keyword search and faster than complete-screen queries. PSDoodle is the first system to allow interactive search of screens via interactive sketching. PSDoodle is built on top of a combination of the Rico repository of some 58k Android app screens, the Google QuickDraw dataset of icon-level doodles, and DoodleUINet, a curated corpus of some 10k app icon doodles collected from hundreds of individuals. In our evaluation with third-party software developers, PSDoodle provided similar top-10 screen retrieval accuracy as the state of the art from the SWIRE line of work, while cutting the average time required about in half.