The processes that regulate star formation within molecular clouds are still not well understood. Various star formation scaling relations have been proposed as an explanation, one of which is to formulate a relation between the star formation rate surface density {Sigma}_SFR_ and the underlying gas surface density {Sigma}_gas_. In this work, we test various star formation scaling relations, such as the Kennicutt-Schmidt relation, the volumetric star formation relation, the orbital time model, the crossing time model and the multi free-fall time-scale model, towards the North American Nebula and Pelican Nebula and in the cold clumps associated with them. Measuring stellar mass from young stellar objects and gaseous mass from CO measurements, we estimate the mean {Sigma}_SFR_, the star formation rate per free-fall time and the star formation efficiency for clumps to be 1.5M_{sun}_/yr/kpc^2^, 0.009 and 2.0 per cent, respectively, while for the whole region covered by both nebulae (which we call the 'NAN' complex) the values are 0.6M_{sun}_/yr/kpc^2^, 0.0003 and 1.6 per cent, respectively. For the clumps, we notice that the observed properties are in line with the correlation obtained between {Sigma}_SFR_ and {Sigma}_gas_, and between {Sigma}_SFR_ and {Sigma}_gas_ per free-fall time and orbital time for Galactic clouds. At the same time, we do not observe any correlation with {Sigma}_gas_ per crossing time and multi free-fall time. Even though we see correlations in the former cases, however, all models agree with each other within a factor of 0.5dex. It is not possible to discriminate between these models because of the current uncertainties in the input observables. We also test the variation of {Sigma}_SFR_ with the dense gas but, because of low statistics, a weak correlation is seen in our analysis.