BUG: dtype silently ignored in MultiIndex constructor

[MarcoGorelli]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

pd.MultiIndex([[1,2,3], [4,5,6]], [[0,1,2], [0,1,2]], dtype='float64')

Issue Description

This outputs

MultiIndex([(1, 4),
            (2, 5),
            (3, 6)],
           )

dtype is ignored

Expected Behavior

I think one of the following:

• dtype is respected
• the dtype argument is removed
• the dtype argument is kept but raises if it's not None

Installed Versions

INSTALLED VERSIONS

commit : 0691c5c
python : 3.12.5
python-bits : 64
OS : Linux
OS-release : 5.15.167.4-microsoft-standard-WSL2
Version : #1 SMP Tue Nov 5 00:21:55 UTC 2024
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : C.UTF-8

pandas : 2.2.3
numpy : 2.2.3
pytz : 2025.1
dateutil : 2.9.0.post0
pip : 24.3.1
Cython : None
sphinx : None
IPython : 8.32.0
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.13.3
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2025.2.0
html5lib : None
hypothesis : None
gcsfs : 2025.2.0
jinja2 : 3.1.5
lxml.etree : None
matplotlib : 3.9.2
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 19.0.0
pyreadstat : None
pytest : 8.3.3
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.14.1
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlsxwriter : None
zstandard : None
tzdata : 2025.1
qtpy : None
pyqt5 : None