I want my boyfriend here

Are Croatia in the EU?
If so, he can come here and will need to get a residence permit. In order to get one you have 4 options.
He has a job (will need to show a contract or some sort of paperwork from the employer)
He is a student studying here (he will need to show course paperwork)
He has sufficient funds to cover himself (equivalent of €10,000)
Family reunification. This is the only one I'm not sure about, I think it takes something like 9 months and costs around 6000DKK (not quite sure on the figures). But this one seemed like a hassle for us (I am English and boyfriend is Danish). Try looking that up online.

Once you have that you get the CPR number

Just so you know. If you choose sufficient funds he is not entitled to claim benefits

It is in EU yes.
I read somewhere that if he is searching for a job he can get a residence permit as well, do you know if thats true? I dont think i remember right

https://www.nyidanmark.dk/da-dkhttp://www.statsforvaltningen.dk/site.aspx?p=4557

Take a look at those two sites, Katrine.

/Nellie

Not that I'm aware of. I moved here in June from England and I had to show them a form filled out by my employer. Unless the Job centre do something similar? Could always give them a call