The ortho and para forms (and A/E forms) have been separated for each of the following molecules: 
H2O, D2O, H2S, D2S, H2D+, D2H+, H2CO, D2CO, c-C3H2, CH3CCH, HCOOCH3, NH2D, D2CS, CH2, NH2,15NH2, H2CS, H2C34S, H2CCO, CH3CCD.
I used the JPL catalog for H2O, D2O, H2S, C3H2, HCOOCH3, NH2D.
I used a file from John Pearson for the D2S molecule. 
I used the CDMS catalog for D2O, H2CO, D2CO, H2D+, D2H+, H2S, D2S, CH3CCH, NH2D, D2CS, CH2, H2CS, NH2,15NH2, H2CCO, CH3OH.
For NH3 and CH3OH in JPL I checked and used the ortho/para/A/E separation performed by S. Yu, J. Pearson L.-H. Xu and B. Drouin.
For CH3CN I used the A and E separation provided by CDMS.

CDMS (Date and Version given in the .cat file provided by CDMS): 
D2S (October 2008, Version 1*)
D2CO (January 2016, Version 3*)
D2O (May 2011, Version 2*)
H2D+ (March 2017, Version 3*)
H2CO (February 2017, Version 3*)
D2H+ (February 2012, Version 2*)
H2S (Oct. 2008, Version 1*)
CH3CCH (August 2008, Version 3*)
c-C3H2 (May 2012, Version 2*)
NH2D (May 2004, Version 1)
CH3CN (Dec. 2009, Version 1*)
D2CS (December 2023, Version 3*)
CH2 (September 2005, Version 1*)
H2CS (January 2019, Version 3*)
H2C-34S (January 2019, Version 2*)
NH2 (October 2001, Version 2)
15NH2 (May 2016, Version 1*)
NH2D-HFS (July 2017)
H2CCO (November 2003, Version 2)
CH3CCD (April 2020, Version 2*)
CH3OH (May 2016, 3*)

JPL:
D2S (Nov. 2005)
H2O (Nov. 2005)
H2S (Nov. 2005)
c-C3H2 (Mar. 2009)
D2O (Nov. 2005)
NH3 (Oct. 2010: S. Yu/J. Pearson/B. Drouin)
CH3OH (Dec. 2010: J. Pearson/L.-H. Xu)
CH3OCHO that I call HCOOCH3 (April 2009: B. Drouin)
CH3CHO (Jan. 2012: H. Pickett, B. Drouin)
NH3-HFS (Oct. 2009: S. Yu, B. Drouin and J. Pearson) from http://spec.jpl.nasa.gov/ftp/pub/catalog/v4/doc/d017002.cat andhttp://spec.jpl.nasa.gov/ftp/pub/catalog/v4/c017002.cat
NH2D (Jan. 1981: H. M. Pickett)

Warnings:
1) In the D2H+ file, they used an incomplete statistical weight: 2(2J+1) for ortho and 2J+1 for para, 
instead of 6(2J+1) and 3(2J+1) respectively. I corrected this in the orthoD2H+.cat and paraD2H+.cat files.
2) The H2O has a number (0) after Qup3 and Qlow3: I removed this number in the orthoH2O.dat and paraH2O.dat 
files, consequently I changed the QNFMT number from 404 to 303.
3) In the D2CO file, they used an incomplete statistical weigth: 3(2J+1) for ortho and 2J+1 for para, instead 
of 6(2J+1) and 3(2J+1) respectively. I corrected this in the orthoD2CO.cat and paraD2CO.cat files to get 
consistent with our catdir.cat.
4) The CDMS D2S file does not take into account the full spin statistical weight (3). It has been corrected 
to get consistent with our catdir.cat. 
5) The CDMS D2O file does not take into account the full spin statistical weight (6(2J+1) for ortho and 
3(2J+1) for para state). It has been corrected, as well as the last column of our catdir.cat for consistency. 
6) The JPL HFS transitions for ortho did not take into account a factor of 3 (14N atom) for the computation of the statistical weigth: 3(2F+1). I manually added this factor in the c018084.cat file. 

The computation of the partition functions at 300,225,150,75,37.5,18.75,9.375 K can be found in the catdir.cat file. Interpolation is made for temperatures inside this range. So LTE model for lower temperatures (e.g. 6 K) can be problematic. However, CASSIS provides also the computation for lower temperatures than 9.375 K and higher than 300 K for many species. The files are provided in the cassis/database/sqlPartitionMole directory as ascii files. If you plan to make a LTE model outside the usual range [9.375-300] K, you should check whether your species is in this directory. For example, in the case of the para c-C3H2 molecule, you can check that the file 38582.txt file in the cassis/database/sqlPartitionMole has a computed partition function as low a 3 K, with a value 2.3 times lower than the value at 9.375 K. By default, CASSIS will use the partition functions provided in this directory.
NB: Q(A/E CH3OH) computed from https://cdms.astro.uni-koeln.de/classic/entries/archive/MeOH/main/vers.3/c032504.egy
 

WARNING: do not compute the Einstein coefficients for the ortho and para forms with the partitions functions at 300K quoted in the catdir.cat file. You have to use the original Q(300K) quoted in the JPL database (that I wrote in the last column of the catdir.cat file). This parameter has been corrected for D2H+, CDMS_D2O, D2CO and CDMS_D2S to take into account the full spin statistical weight. The main interest of having those Q(Tex) for each symmetry, is an accurate computation for the column density for a symmetry state, or in the case of Cassis, computation of the main beam temperature for a line of a certain symmetry.