If we examine the CCES data, we can split out the responses by state (plus D.C.) and examine the responses to the party-identification, 'pid3' question. In addition, the CCES provides a weight variable that we can apply to the data to ensure we're getting a representative sample of each state's population - according to the CCES FAQ, "State is one of the variables used to construct the target population".
Having done so, we arrive at the following results - unsurprisingly, Washington D.C. is at the top of our list, with a Democratic lead of 62.1 percentage points, while Wyoming, Utah, and Idaho sit at the bottom, with a Republican lead of between 20 and 30 percentage points.

Below are the full results - note that the respondent totals (Democrat, Republican, Independent, & Other columns) are not integers because weighting has been applied to each response. The code used in this answer can be found on GitHub.
| State | Democrat | Republican | Independent | Other | Democrat lead (pp) |
| ----- | --------- | ---------- | ----------- | -------- | ------------------ |
| DC | 144.1256 | 16.4052 | 38.9692 | 6.1695 | 62.1 |
| MD | 516.6171 | 209.0855 | 287.9373 | 34.3685 | 29.3 |
| HI | 73.9223 | 28.1528 | 53.312 | 2.0263 | 29.1 |
| NY | 1657.1569 | 763.2634 | 862.7511 | 119.4693 | 26.3 |
| MA | 426.8993 | 149.1443 | 472.6593 | 37.9207 | 25.6 |
| CA | 2166.7948 | 1001.9362 | 1301.8215 | 171.5298 | 25.1 |
| NJ | 666.5909 | 391.3402 | 362.4723 | 35.5307 | 18.9 |
| CT | 214.6217 | 117.1562 | 200.165 | 18.6369 | 17.7 |
| IL | 875.2273 | 540.4494 | 558.9122 | 73.8036 | 16.3 |
| NV | 267.3017 | 169.676 | 161.746 | 20.6641 | 15.8 |
| NM | 134.1839 | 84.6754 | 85.9973 | 13.4963 | 15.6 |
| WA | 472.9804 | 298.585 | 403.5352 | 66.2484 | 14.0 |
| VA | 642.0327 | 413.4867 | 527.3681 | 58.9686 | 13.9 |
| VT | 41.6948 | 28.1073 | 50.2078 | 10.5828 | 10.4 |
| MN | 310.3748 | 223.4849 | 278.6167 | 42.642 | 10.2 |
| OR | 276.8067 | 201.4501 | 217.7284 | 56.816 | 10.0 |
| RI | 50.238 | 35.7148 | 74.0402 | 12.0557 | 8.4 |
| DE | 84.0697 | 68.1179 | 45.9298 | 7.7521 | 7.7 |
| CO | 297.5239 | 234.4486 | 380.2379 | 53.2942 | 6.5 |
| MI | 592.2295 | 493.3579 | 494.1535 | 59.8103 | 6.0 |
| NH | 97.1591 | 79.3347 | 149.4676 | 6.3508 | 5.4 |
| ME | 107.2735 | 91.3964 | 92.8959 | 20.0682 | 5.1 |
| NC | 619.4692 | 556.286 | 514.2729 | 54.6624 | 3.6 |
| PA | 1024.2002 | 964.2995 | 604.0254 | 88.5159 | 2.2 |
| FL | 1479.8972 | 1401.8382 | 1133.7669 | 142.5409 | 1.9 |
| TX | 1609.3756 | 1537.9015 | 1277.2314 | 165.7263 | 1.6 |
| GA | 706.6904 | 678.938 | 512.2127 | 71.6373 | 1.4 |
| AZ | 413.9019 | 409.9541 | 430.5206 | 36.4067 | 0.3 |
| MS | 176.0888 | 175.9591 | 106.9773 | 9.9933 | 0.0 |
| WI | 342.6163 | 359.7882 | 355.5616 | 29.9576 | -1.6 |
| OH | 731.1436 | 849.8178 | 750.6494 | 80.4408 | -4.9 |
| IA | 160.7683 | 188.7934 | 158.6184 | 14.8585 | -5.4 |
| MT | 42.5388 | 54.2012 | 81.5566 | 17.8502 | -5.9 |
| SD | 49.7726 | 59.5059 | 37.0646 | 2.9229 | -6.5 |
| SC | 309.8232 | 391.6238 | 323.4282 | 37.663 | -7.7 |
| AK | 19.9546 | 29.896 | 48.9126 | 12.0621 | -9.0 |
| TN | 384.9425 | 546.0095 | 357.0397 | 78.6189 | -11.8 |
| MO | 361.4005 | 512.1197 | 340.5616 | 33.5587 | -12.1 |
| AL | 278.5807 | 397.0025 | 248.725 | 26.703 | -12.5 |
| IN | 353.8866 | 526.7265 | 371.4587 | 59.787 | -13.2 |
| LA | 174.2027 | 257.2736 | 170.8912 | 17.9018 | -13.4 |
| NE | 73.885 | 117.8483 | 98.2564 | 19.2076 | -14.2 |
| KS | 113.4378 | 182.9865 | 113.5916 | 30.0774 | -15.8 |
| AR | 126.0329 | 223.5942 | 212.3144 | 32.24 | -16.4 |
| OK | 158.8235 | 261.5316 | 178.4956 | 19.1745 | -16.6 |
| KY | 281.7643 | 442.3613 | 198.19 | 35.7097 | -16.8 |
| WV | 94.6795 | 169.814 | 139.3239 | 17.9713 | -17.8 |
| ND | 38.7878 | 69.7398 | 39.0292 | 9.4948 | -19.7 |
| WY | 19.1726 | 37.157 | 25.9175 | 6.4899 | -20.3 |
| UT | 76.6741 | 197.936 | 160.3991 | 27.8248 | -26.2 |
| ID | 48.5451 | 140.4214 | 107.9066 | 20.7542 | -28.9 |