Recent work in crosslingual semantic parsing has successfully applied machine translation to localize accurate parsing to new languages. However, these advances assume access to high-quality machine translation systems, and tools such as word aligners, for all test languages. We remove these assumptions and study cross-lingual semantic parsing as a zero-shot problem without parallel data for 7 test languages (DE, ZH, FR, ES, PT, HI, TR). We propose a multi-task encoder-decoder model to transfer parsing knowledge to additional languages using only English-Logical form paired data and unlabeled, monolingual utterances in each test language. We train an encoder to generate language-agnostic representations jointly optimized for generating logical forms or utterance reconstruction and against language discriminability. Our system frames zero-shot parsing as a latent-space alignment problem and finds that pre-trained models can be improved to generate logical forms with minimal cross-lingual transfer penalty. Experimental results on Overnight and a new executable version of MultiATIS++ find that our zero-shot approach performs above back-translation baselines and, in some cases, approaches the supervised upper bound.