Kosovo has not yet defined a particular policy on this topic.
According to its Ministry of Foreign Affairs, there is no distinction based on the citizenship. Every citizen may therefore enter the country and stay for a maximum of 90 days. However, there are some rules to respect. You should be able to :
- Have some valid travel documents (thus coming from a not recognized country may be an issue)
- Prove you can pay for your expenses
- Prove you will exit the territory (for example, having a return ticket)
- Give a reason for travelling to Kosovo
After 90 days, a traveller must contact the Kosovo police to be registered, but it is unclear if the right to stay will be granted.
EDIT : See @Janusz answer, as the policy is now defined and EU citizens can enter with an ID card.