The ultimate goal of enabling sensing through the cellular network is to obtain coordinated sensing of an unprecedented scale, through distributed integrated sensing and communication (D-ISAC). This, however, introduces challenges related to synchronization and demands new transmission methodologies. In this paper, we propose a transmit signal design framework for D-ISAC systems, where multiple ISAC nodes cooperatively perform sensing and communication without requiring phase-level synchronization. The proposed framework employing orthogonal frequency division multiplexing (OFDM) jointly designs downlink coordinated multi-point (CoMP) communication signals and multi-input multi-output (MIMO) radar signals, leveraging both collocated and distributed MIMO radars to estimate angle-of-arrival (AOA) and time-of-flight (TOF) from all possible multi-static measurements for target localization. To design the optimal D-ISAC transmit signal, we use the target localization Cram\'er-Rao bound (CRB) as the sensing performance metric and the signal-to-interference-plus-noise ratio (SINR) as the communication performance metric. Then, an optimization problem is formulated to minimize the localization CRB while maintaining a minimum SINR requirement for each communication user. Moreover, we present three distinct transmit signal design approaches, including optimal, orthogonal, and beamforming designs, which reveal trade-offs between ISAC performance and computational complexity. Unlike single-node ISAC systems, the proposed D-ISAC designs involve per-subcarrier sensing signal optimization to enable accurate TOF estimation, which contributes to the target localization performance. Numerical simulations demonstrate the effectiveness of the proposed designs in achieving flexible ISAC trade-offs and efficient D-ISAC signal transmission.