  We give a description of double parton scattering with measured transverse
momenta in the final state, extending the formalism for factorisation and
resummation developed by Collins, Soper and Sterman for the production of
colourless particles. After a detailed analysis of their colour structure, we
derive and solve evolution equations in rapidity and renormalisation scale for
the relevant soft factors and double parton distributions. We show how in the
perturbative regime, transverse momentum dependent double parton distributions
can be expressed in terms of simpler nonperturbative quantities and compute
several of the corresponding perturbative kernels at one-loop accuracy. We then
show how the coherent sum of single and double parton scattering can be
simplified for perturbatively large transverse momenta, and we discuss to which
order resummation can be performed with presently available results. As an
auxiliary result, we derive a simple form for the square root factor in the
Collins construction of transverse momentum dependent parton distributions.
