  We present two methods to determine whether the interactions in a
Tomonaga-Luttinger liquid (TLL) state of a spin-$1/2$ Heisenberg
antiferromagnetic ladder are attractive or repulsive. The first method combines
two bulk measurements, of magnetization and specific heat, to deduce the TLL
parameter that distinguishes between the attraction and repulsion. The second
one is based on a local-probe, NMR measurements of the spin-lattice relaxation.
For the strong-leg spin ladder compound $\mathrm{(C_7H_{10}N)_2CuBr_4}$ we find
that the isothermal magnetic field dependence of the relaxation rate,
$T_1^{-1}(H)$, displays a concave curve between the two critical fields that
bound the TLL regime. This is in sharp contrast to the convex curve previously
reported for a strong-rung ladder $\mathrm{(C_5H_{12}N)_2CuBr_4}$. Within the
TLL description, we show that the concavity directly reflects the attractive
interactions, while the convexity reflects the repulsive ones.
