  We present a JWST/NIRCam transmission spectrum from $3.9-5.0$ $\mu$m of the
recently-validated sub-Earth GJ 341b ($\mathrm{R_P} = 0.92$
$\mathrm{R_{\oplus}}$, $\mathrm{T_{eq}} = 540$ K) orbiting a nearby bright M1
star ($\mathrm{d} = 10.4$ pc, $\mathrm{K_{mag}}=5.6$). We use three independent
pipelines to reduce the data from the three JWST visits and perform several
tests to check for the significance of an atmosphere. Overall, our analysis
does not uncover evidence of an atmosphere. Our null hypothesis tests find that
none of our pipelines' transmission spectra can rule out a flat line, although
there is weak evidence for a Gaussian feature in two spectra from different
pipelines (at 2.3 and $2.9\sigma$). However, the candidate features are seen at
different wavelengths (4.3 $\mu$m vs 4.7 $\mu$m), and our retrieval analysis
finds that different gas species can explain these features in the two
reductions (CO$_2$ at $3.1\sigma$ compared to O$_3$ at $2.9\sigma$), suggesting
that they are not real astrophysical signals. Our forward model analysis rules
out a low mean molecular weight atmosphere ($< 350\times$ solar metallicity) to
at least $3\sigma$, and disfavors CH$_4$-dominated atmospheres at $1-3\sigma$,
depending on the reduction. Instead, the forward models find our transmission
spectra are consistent with no atmosphere, a hazy atmosphere, or an atmosphere
containing a species that does not have prominent molecular bands across the
NIRCam/F444W bandpass, such as a water-dominated atmosphere. Our results
demonstrate the unequivocal need for two or more transit observations analyzed
with multiple reduction pipelines, alongside rigorous statistical tests, to
determine the robustness of molecular detections for small exoplanet
atmospheres.
