We investigate the observed relationship between black hole mass ($M_{rm BH}$), bolometric luminosity ($L_{rm bol}$), and Eddington ratio (${lambda}_{rm Edd}$) with optical emission line ratios ([NII] {lambda}6583/H{alpha}, [SII] {lambda}{lambda}6716,6731/H{alpha}, [OI] {lambda}6300/H{alpha}, [OIII] {lambda}5007/H{beta}, [NeIII] {lambda}3869/H{beta}, and HeII {lambda}4686/H{beta}) of hard X-ray-selected AGN from the BAT AGN Spectroscopic Survey (BASS). We show that the [NII] {lambda}6583/H{alpha} ratio exhibits a significant correlation with ${lambda}_{rm Edd}$ ($R_{rm Pear}$ = -0.44, $p$-value=$3times10^{-13}$, {sigma} = 0.28 dex), and the correlation is not solely driven by $M_{rm BH}$ or $L_{rm bol}$. The observed correlation between [NII] {lambda}6583/H{alpha} ratio and $M_{rm BH}$ is stronger than the correlation with $L_{rm bol}$, but both are weaker than the ${lambda}_{rm Edd}$ correlation. This implies that the large-scale narrow lines of AGN host galaxies carry information about the accretion state of the AGN central engine. We propose that the [NII] {lambda}6583/H{alpha} is a useful indicator of Eddington ratio with 0.6 dex of rms scatter, and that it can be used to measure ${lambda}_{rm Edd}$ and thus $M_{rm BH}$ from the measured $L_{rm bol}$, even for high redshift obscured AGN. We briefly discuss possible physical mechanisms behind this correlation, such as the mass-metallicity relation, X-ray heating, and radiatively driven outflows.
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