This is the sort of thing I could have done at my most mentally unwell (just out of abusive childhood, obsessive, drug-taking, borderline psychosis at times).
I was functioning very well on the outside, holding down a fulltime job, rising slowly through academic and then professional ranks. But this was peppered with periods of really being very unwell.
One of the things that used to happen was that I would suddenly get really fixated on someone. Usually someone I would see semi-regularly, but not enough to develop anything beyond an acquaintance relationship (actually always more distant colleagues in my case).
They would become idolised in my head as "the answer" to everything. The potential source of the love I craved, the inspiration to turn my life around, become cleaner-living, this would spiral until I was virtually seeing them as some sort of Messiah, destined to save me and love me.
Then would come a sort of stalking hunt as I tried to make fantasy materialise into reality. Internet stalking of them, their email address, and absolutely any names I could find connected to them. Even paid for those more detailed 192 type searches to get details of previous people they lived with.
I'd also watch them, take covert photos, nothing compromising (not proud of this), write down every location and time I ever saw them, etc etc.
All really terrifyingly abnormal now I look back at it. Fortunately, it never progressed beyond the steps laid out above. I either became so unwell it was time for an inpatient stint, or the obsession kind of fizzled out as quickly as it began.
However, I know exactly where my thoughts were leading me in terms of next step... and it would have been something like what this woman has potentially done. Identify barriers to our "destined" relationship and remove them.
I think involving the police is absolutely the right thing to do. I don't know for sure if this (unwell woman) is the case in your scenario, but I can bear firsthand witness to the fact that it's definitely possible.