Green’s Dictionary of Slang

nautch n.

also nauch, nautchery, nautch house, nautch joint
[Urdu/Hind. n?ch, dancing, usu. as an exhibition of Indian dancing, thus a nautch girl, a dancing girl; the image of the ‘exotic’ East led inevitably to assumptions of sexual licence + house n.1 (1)/joint n. (1)]

(US) a brothel; also attrib.

[[Ind]Hicky’s Bengal Gaz. 4-11 Aug. n.p.: She entertains me with a Calpootly notch until four].
[[Ind]Bellew Memoirs of a Griffin II 32: A jocular imitation of the Indian nautch girls, with whom this song is a favourite].
[US]Ellsworth Reporter 28 Mar. in Miller & Snell Why the West was Wild 633: She left the farm, resumed her occupation as Madam of the ‘nauch’.
[US]Hostetter & Beesley It’s a Racket! 232: nautch house – Establishment, either apartment, home, or hotel, where professional or clandestine prostitutes or immoral women live or can be met.
[US]S.J. Perelman in Marschall That Old Gang o’ Mine (1984) 112: The great news was brought in by a nautch dancer.
[US]D. Maurer ‘Prostitutes and Criminal Argots’ in Lang. Und. (1981) 117/1: bull pen. A cheap house. Also cathouse, hook-shop, nanny-shop, nautch house.
[US]Goldin et al. DAUL 144/1: Nautchery. A brothel. [...] Nautch-joint. A house of prostitution.
[US](con. 1870s) Miller & Snell Why the West was Wild 13: Ellsworth’s was known as ‘Scragtown’ and ‘Nauchville’.
[US]Trimble 5000 Adult Sex Words and Phrases.
[US]Maledicta IX 150: The original argot of prostitution includes some words and phrases which have gained wider currency and some which have not […] nautch joint.

In compounds

nautch broad (n.) [broad n.2 (2)]

(US) a prostitute working in a brothel.

[US]Goldin et al. DAUL 144/1: Nautch-broad. A prostitute working in a brothel, not soliciting on streets.
nautch show (n.)

in carnival use, a more than usually sexualized ‘girl show’.

[US]W. Keyser ‘Carny Lingo’ in http://goodmagic.com 🌐 Nautch Show — A girl show with particularly raunchy acts.