They were interviewed under caution and released without charge.
The investigation relates to matters which previously led to findings that Deputy St Pier had broken the States members' code of conduct.
As recently as last Thursday, the States Assembly rejected a recommendation from its standards commissioner to suspend Deputy St Pier over a phone call with a national journalist who was preparing a story concerning complaints about local paediatric services.
'On the morning of 3 December, Guernsey Police arrested both a 58-year-old man and a 58-year-old woman on suspicion of harassment,' police said in a statement issued just before 4pm today.
'Enquiries are now ongoing, and no further comment will be provided while the investigation continues.'
Minutes earlier, Deputy St Pier released a statement of his own, after becoming aware that rumours were circulating.
'My wife and I are the subjects of an investigation following a complaint alleging harassment. This is a shocking allegation which we completely refute,' he said.
'We were arrested on 3 December, just six days after my exoneration by the States when the Assembly voted overwhelmingly to reject my proposed suspension in respect of an earlier complaint.
'We have stated unequivocally that we deny any wrongdoing whatsoever. Following interviews under caution, we were released without charge. The interviews did not refer to any material information that is not already in the public domain.
'This week we naively imagined that we could finally move on with our lives after nearly four years of complaints being lodged against me.
'We are hopeful that this will be the end of the matter.
'As I said in closing my speech last week, I will continue to represent the interests of those who wish me to do so and to press for systemic and cultural change in our healthcare systems.'
Deputy St Pier's statement made no mention of the roles he holds in the States, but it is understood that he intends to continue as Policy & Resources' vice-president and treasury lead.
‘Our committee has been informed that Deputy St Pier was arrested on Wednesday morning on suspicion of harassment,‘ said president Lindsay de Sausmarez in a statement on behalf of P&R.
‘I am currently off-island, representing Guernsey at the British Irish Council in Wales, so the other members of P&R and I have not yet had a chance to discuss this matter.
‘We will consider it at the earliest opportunity and will provide an update once we have done so. Please bear with us in the meantime,’ she said.
