Is there any text in any of the Harry Potter books that identifies which floor of Hogwarts Castle the entrance to the Library is located in?
First Floor. (Second Floor in American-speak.)
It is one floor below the entrance to Dumbledore's office, which is on the second floor.
Harry Potter and the Goblet of Fire - Page 557
Harry tore up the stone steps, through the oak front doors and off up the marble staircase towards the second floor. Five minutes later, he was hurtling toward a stone gargoyle standing halfway along an empty corridor. "Sher --sherbet lemon!" he panted at it. This was the password to the hidden staircase to Dumbledore's office...
Harry Potter and the Chamber of Secrets - Page 150
[Harry] turned on his heel and stormed out of the library, earning himself a reproving glare from Madam Pince, who was polishing the gilded cover of a large spellbook. Harry blundered up the corridor...
Harry Potter and the Chamber of Secrets - Page 151
Harry stamped up the stairs and turned along another corridor, which was particularly dark; the torches had been extinguished by a strong, icy draught which was blowing through a loose window pane. He was halfway down the passage...
Harry Potter and the Chamber of Secrets - Page 152
They marched in silence around a corner and she stopped before a large and extremely ugly stone gargoyle.