The harem part comes by way of the zombie protagonist Ayumu who lives with the silent necromancer who resurrected Ayumu after being killed by a supernatural serial killer. Ayumu starts out at the beginning of the show looking for the person who killed him and along the way he accidentally steals the powers of a magical girl and has to become a trap magical girl in order to battle demons who are invading earth. The magical girl moves in so that she can figure out how to get her powers back.
Then the ninja vampire shows up to kill the necromancer but she fails at her job and decides to move in as well. Now poor Ayumu's house is full of girls as he tries to survive school the rigurs of being a trap magical girl and of course the hardships of being a zombie all the while being called a pervert and being methodically killed and put back together every episode.
half way through Ayumu solves the mystery of the serial killer and even adds another ninja vampire to the harem and this one even announces that Ayumu is her betrothed thanks to an accidental kiss. But don't worry another bad guy makes an appearance to keep things interesting. This time around it's another Zombie that the necromancer created. This one however wants the necromancer to kill him and will do anything to achieve his ends.
Ayumu and his supernatural harem defeat the other Zombie and save the necromancer and enjoy a bit of a fun time at a water park that turns into fanservice overload episode when Ayumu gets the necromancers powers for a little bit and wishes that everyone can look super cute. It was a fun little extra that didn't have anything to do with rest of the series and neither did the ova which was a duel story episode that featured the ninja vampires horrid cooking skills and
The series was simulcast on Crunchyroll but is no longer available but you will be able to catch later when it's released by FUNimation who did license the series. In the mean time you can check out the trailer for the series below. Oh and there is a second season in the works as well.