Does dropping a Coursera course look bad in a PhD application to the university offering the course? A few weeks ago I've enrolled in a Coursera course offered by university A, without asking for a certificate. I've completed some of the work, but now my university holds a course on the same topic, to which I am enrolled for credit. 
Consequently, I decided to stop doing assignments from the Coursera course and focus on the course I'm enrolled in.

University A is one of the universities I am planning to apply to for my PhD studies next year, possibly in the topic of the course (or even with the professor teaching it).

How likely is it that the professor and/or the committee will check whether I've already been enrolled in something offered by them, and will get a bad impression because of me dropping the course? (e.g they might conclude that I'm not serious/committed when it comes to studying.)

Do committees generally look for academic information on applicants other than in the documents they provide in their application?
AFAIK Coursera is not for credit, thus should not impact your phd record in any way.