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

眠い-----状態（じょうたい） 眠たい--欲求（よっきゅう）

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。

almost the same and you can use it alternately.