GRB 070201 was a bright, short-duration, hard-spectrum gamma-ray burst detected by the Interplanetary Network. Its error quadrilateral, which has an area of 0.124 deg2, intersects some prominent spiral arms of the nearby M31 (Andromeda) galaxy. Given the properties of this GRB, along with the fact that LIGO data argue against a compact binary merger origin in M31, it is an excellent candidate to have been an extragalactic soft gamma-ray repeater (SGR) giant flare, with an energy of 1.4 × 1045 ergs. However, we cannot rule out the possibility that it was a short-duration GRB in the background. Analysis of ROTSE-IIIb visible-light observations of M31, taken 10.6 hr after the burst and covering 42% of the GRB error region, does not reveal any optical transient down to a limiting magnitude of 17.1. We inspected archival and proprietary XMM-Newton X-ray observations of the intersection of the GRB error region and M31, obtained about 4 weeks prior to the outburst, in order to look for periodic variable X-ray sources. No SGR or anomalous X-ray pulsar (AXP) candidates (periods in the range 1-20 s) were detected. We discuss the possibility of detecting extragalactic SGRs/AXPs by identifying their periodic X-ray light curves. Our simulations suggest that the probability of detecting the periodic X-ray signal of one of the known Galactic SGRs/AXPs, if placed in M31, is about 10% using a 50 ks XMM-Newton exposure, increasing to 50% for a 2 Ms observation.