No [CII] or dust detection in two Little Red Dots at z$_{\rm spec}$ > 7

Little Red Dots (LRDs) are compact, point-like sources characterized by their red color and broad Balmer lines, which have been debated to be either dominated by active galactic nuclei (AGN) or dusty star-forming galaxies (DSFGs). Here we report two LRDs (ID9094 and ID2756) at z$_{\rm spec}$>7, recently discovered in the JWST FRESCO GOODS-North field. Both satisfy the "v-shape" colors and compactness criteria for LRDs and are identified as Type-I AGN candidates based on their broad H$\beta$ emission lines (full width at half maximum: 2280$\pm$490 km/s for ID9094 and 1070$\pm$240 km/s for ID2756) and narrow [OI] lines ($\sim$ 300-400 km/s). To investigate their nature, we conduct deep NOEMA follow-up observations targeting the [CII] 158${\rm \mu m}$ emission line and the 1.3 mm dust continuum. We do not detect [CII] or 1.3 mm continuum emission for either source. Notably, in the scenario that the two LRDs were DSFGs, we would expect significant detections: $>16\sigma$ for [CII] and $>3\sigma$ for the 1.3 mm continuum of ID9094, and $>5\sigma$ for [CII] of ID2756. Using the 3$\sigma$ upper limits of [CII] and 1.3 mm, we perform two analyses: (1) UV-to-FIR spectral energy distribution (SED) fitting with and without AGN components, and (2) comparison of their properties with the L$_{[CII]}$-SFR$_{tot}$ empirical relation. Both analyses are consistent with a scenario where AGN activity may contribute to the observed properties, though a dusty star-forming origin cannot be fully ruled out. Our results highlight the importance of far-infrared observations for studying LRDs, a regime that remains largely unexplored.