Hi. The local authority is completely separate to the PCT. If they are health notes, which it sounds as if they are, the LA won't have anything to do with them due to data protection, confidentiality and information sharing laws.
Child protection is taken very seriously in PCTs and most HCPs would prefer to wrongly have a concern rather than overlook something. Most PCTs have safeguarding teams which can be accessed for advice only. I have accessed such teams for advice, keeping the child / family I've had a concern about anonymous to protect their confidentiality whilst seeking this advice. If the safeguarding team don't feel further action is needed, it will be left as is. It does need to be documented, though, to ensure the records are complete and accurate. It is also documented in case further concerns arise in the future (quite often in child protection cases an isolated incident may not seem a concern until it is seen in light of other information so all concerns need to be documented).
HCPs will also document everything so, if need be (e.g. if there is ever a serious case review) it can be proven they have followed procedure and sought appropriate advice...even if their original concern is later thought to be unfounded or inaccurate.
I haven't in the past discussed concerns with parents as, after seeking advice from the safeguarding team, it turned out it wasn't truly a child protection concern after all. To have discussed it would have been premature, it would not have been of any use and, as another poster mentioned, would have undermined the working relationship. It was purely something I needed to seek advice on.
If true child protection concerns were identified and further action needed to be taken (i.e. referral to social care) this would be discussed with parents unless it put the child in further danger.
I know it may seem shocking that a HCP had a concern about you and your child but they were following correct child protection procedures. They obviously came to the conclusion it was inaccurate and unfounded as no further action was taken.