This could be because the WRITE_EXTERNAL_STORAGE permission has been made conditional (from build 4150 the permission is only requested for older Android versions below API level 19 (Kitkat)). If you have a CM12.1 with the external storage writeable to apps (not possible on a normal Android), this might lead to the crash.
I've now downloaded 3.1.1 build 4149 from some strange apk collection website, works like a charm on this fresh install of CM 12.1 on I9300 (had to buy a fresh key, but as I like the app very much it's worth it), so there must be some kind of regression in 4151/4152. Feedback with logs uploaded after crash. I've disabled updates, will check back in a while.
Well. Bad luck. I've gone from Stock S3 to CM 12.1 and at the same time caught Build 4151 - during start it didn't find the sd card !? - but now after installing the post-21:30 update it doesn't even start. Too bad. I'm addicted to your app for years.
This evening, a broken release has been published on Google Play (Build 4151). A fix has been already uploaded and will be available on Google Play in about 1/2 hour (21:30 CET). Sorry for the trouble...