Let us clarify one thing at first.
Nobody worships a statue unless he/she is mentally unstable. People that seem doing so are actually trying to show respect to some beings that are represented by those statues. This act is shirk. According to Quran, shirk means attributing some special qualities to a being as if he/she/it is superior to others by unnatural means but still lower than the Almighty. This is strictly forbidden and it is the greatest sin that is described in Quran.
Now let’s come to the situation you ask about.
There is always a specific motivation in placing a piece of art in some place, especially a statue. The lightest of it may be admiring the piece and also for sure, its artist. If you think for a moment, you will figure out that you are actually admiring the creativity of the artist. His/her intelligence, ideas and style… These things that you feel about an artist when you look at his/her works are exactly the feelings that you are ordered to dedicate to the Creator who created everything including the fascinating human mind, with which all kinds of art and science is being made. That’s why; an act like this will be getting too close to shirk. It will be like walking very near to the edge of a cliff. Walking near to the edge of a cliff is a dangerous act indeed. It is very close to death. Therefore, placing a statue to someplace is, in terms of Islamic Law, makruh tahrimi. It means “an act that is close to haram”.
This ruling above is for “placing a statue for decoration”.
Placing statues of existed persons to glorify them is -Allah knows the best- pure shirk.