Website:
http://www.commondeerpress.com/
The site looks decent and none of the text raises red flags (at least not with me); however, there also isn't much information to go off of.
Their Twitter and Facebook pages were both started on February 28th of this year, so they are a new press.
I checked their Facebook page and they've posted a PW announcement of a novelette being bought by Ellie Sipila of Common Deer Press. I went to Ellie Sipila's Twitter page and she states that she's a senior editor for Book Fish Books. I checked out the Book Fish Books site and they seem to have no affiliation with Common Deer Press. Ellie Sipila's Twitter feed also doesn't mention Common Deer Press.
I found a page for them at Publishers Marketplace, where Ellie Sipila is listed as the acquisitions editor:
https://www.publishersmarketplace.com/members/CommonDeerPress/. The page states "We are experienced editors, designers, production managers, and marketers", but it's not clear who "We" are. So far, Ellie Sipila is the only person I've found to be associated with the Press. The page also has her name specifically listed as the page title, above the press's name at the top. Right now, she appears to be the only member of the organization and the information leads me to believe she heads the company. With that being the case, it's weird she hasn't mentioned it on any of her social media accounts.
Overall, this looks like it could be a cool press, but so far there is too little information to tell. I would want to know who else is a part of the operation before submitting anything to them.