Is there any difference between 眠い and　眠たい?

Question

Answer

眠い(nemui) adjective ＝　眠たい(nemutai) adjective　＝　sleepy
眠りたい(nemuri-tai) verb+auxiliary verb = want to sleep, would like to sleep

Answer

眠い-----状態（じょうたい）
眠たい--欲求（よっきゅう）

Answer

眠い is sleepy
but 眠たい is want to sleep

Maybe there is a circumstance : 
I am sleepy but I have jobs to do, so I don't want to sleep.
私は眠い、でも仕事があります、そう寝たくない。

Answer

almost the same and you can use it alternately.